A map is a visual representation of an area—a symbolic depiction highlighting relationships between elements of that space such as objects, regions, and themes. A raised-relief map or terrain model is a three-dimensional representation usually of terrain For other uses of Object see Object. In Philosophy, an object is a thing an Entity, or a Being. The article is about the geographic sense of the term For other uses including Regions and Regional, see Region (disambiguation.
Many maps are static two-dimensional, geometrically accurate representations of three-dimensional space, while others are dynamic or interactive, even three-dimensional. A 2D geometric model is a Geometric model of an object as two-dimensional figure usually on the Euclidean or Cartesian plane. Three-dimensional space is a geometric model of the physical Universe in which we live Although most commonly used to depict geography, maps may represent any space, real or imagined, without regard to context or scale; e. Space is the extent within which Matter is physically extended and objects and Events have positions relative to one another ConTEXT is a closed-source Freeware Text editor for Microsoft Windows, aimed at software developers The scale of a Map is the ratio of a single unit of distance on the map to the equivalent distance on the ground g. Brain mapping, DNA mapping, and extraterrestrial mapping. Brain mapping is a set of Neuroscience techniques predicated on the Mapping of (biological quantities or properties onto spatial representations of the (human or Deoxyribonucleic acid ( DNA) is a Nucleic acid that contains the genetic instructions used in the development and functioning of all known
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Geographic maps
Cartography, or map-making is the study and, often, practice, of crafting representations of the Earth upon a flat surface (see History of cartography), and one who makes maps is called a cartographer. Cartography or mapmaking (in Greek chartis = map and graphein = write has been an integral part of the human story for a long time (maybe 8000 years
Road maps are perhaps the most widely used maps today, and form a subset of navigational maps, which also include aeronautical and nautical charts, railroad network maps, and hiking and bicycling maps. A nautical chart is a graphic representation of a maritime area and adjacent Coastal regions In terms of quantity, the largest number of drawn map sheets is probably made up by local surveys, carried out by municipalities, utilities, tax assessors, emergency services providers, and other local agencies. A municipality is an administrative entity composed of a clearly defined territory and its population and commonly denotes a City, Town, or Village, or Many national surveying projects have been carried out by the military, such as the British Ordnance Survey (now a civilian government agency internationally renowned for its comprehensively detailed work). The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located Ordnance Survey (OS is an Executive agency of the United Kingdom government
A map can also be any document giving information as to where or what something is.
Orientation of maps
The term orientation refers to the relationship between directions on a map and compass directions. For other uses see Orientation. Orientation means direction of some axis or vector or pseudo-vector The word orient is derived from oriens, meaning east. The Orient is a term which simply means the " East " It originated in Western Asia to describe that part of the world In the Middle Ages many maps, including the T and O maps, were drawn with east at the top. Today the most common, but far from universal, cartographic convention is that North is at the top of a map. This is about the direction for other uses see North (disambiguation. Examples of maps not oriented to north are:
- Reversed maps, also known as Upside-Down maps or South-Up maps, which generally show Australia and New Zealand at the top of the map instead of the bottom. A reversed map, also known as an Upside-Down map or South-Up map, is a World map that generally shows Australia and New Zealand
- Polar maps of the Arctic or Antarctic regions are conventionally centred on the pole, in which case the direction north would be towards or away from the centre of the map, respectively. The azimuthal equidistant projection is a particular Map projection. The Arctic is the Region around the Earth 's North Pole, opposite the Antarctic region around the South Pole.
- Buckminster Fuller's Dymaxion maps are based on a projection of the Earth's sphere onto an icosahedron. Richard Buckminster “Bucky” Fuller ( July 12, 1895 &ndash July 1, 1983) was an American Architect, Author The Dymaxion map of the Earth is a projection of a global map onto the surface of a Polyhedron, which can then be unfolded to a net In Geometry, an icosahedron ( Greek: eikosaedron, from eikosi twenty + hedron seat /ˌaɪ The resulting triangular pieces may be arranged in any order or orientation.
- Maps from non-Western traditions are oriented a variety of ways. Old maps of Edo show the Japanese imperial palace as the "top", but also at the centre, of the map. literally bay - Door, " Estuary " edo once also spelled Yedo or Yeddo, is the is the imperial main residence of the Emperor of Japan. It is a large park-like area located in Chiyoda Tokyo close to Tokyo Station and contains various buildings Labels on the map are oriented in such a way that you cannot read them properly unless you put the imperial palace above your head.
- Medieval European T and O maps such as the Hereford Mappa Mundi were centred on Jerusalem with east at the top. A T and O map or O-T or T-O map ( orbis terrae, orb or circle of the earth is a type of Medieval World map, sometimes also called The Hereford Mappa Mundi is a T and O map derivate, dating to ca Jerusalem (יְרוּשָׁלַיִם, he-Latn Yerushaláyim; Arabic: ar القُدس, ar-Latn al-Quds) is the Indeed, prior to the reintroduction of Ptolemy's Geography to Europe around 1400, there was no single convention in the West. Claudius Ptolemaeus ( Greek: Klaúdios Ptolemaîos; after 83 &ndash ca Portolan charts, for example, are oriented to the shores they describe. A portolan (derived from the Latin word portus, port is an early modern European navigation chart, dating from the Thirteenth century or later
- Route and channel maps have traditionally been oriented to the road or waterway they describe.
- Many maps used in the Society for Creative Anachronism show the west at the top, in honour of the Society starting in California. Society for Creative Anachronism (usually shortened to SCA) is a historical re-creation and Living history group founded in 1966 which California ( is a US state on the West Coast of the United States, along the Pacific Ocean.
Scale and accuracy
Many but not all maps are drawn to a scale, expressed as a ratio such as 1:10,000, meaning that 1 of any unit of measurement on the map corresponds to 10,000 of that same unit in reality. The scale of a Map is the ratio of a single unit of distance on the map to the equivalent distance on the ground A ratio is an expression which compares quantities relative to each other Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as Reality, in everyday usage means "the state of things as they actually exist" This allows the reader to estimate the sizes of, and distances between, depicted objects. A larger scale (i. e. the second number of the ratio is smaller) shows more detail and supports more accurate estimates, thus requiring a larger map to show the same area. Highly detailed maps covering areas ranging upward in size from small cities or counties to entire countries or continents are now often published as books, or computer software (with numerous tools to aid the user, including user-adjustable scale and customized search engines), for convenient handling. A city is an Urban area with a large Population and a particular Administrative, Legal, or Historical status A county is a Land area of Regional Government within a larger State. In Political geography and International politics, a country is a Political division of a geographical entity A continent is one of several large Landmasses on Earth. They are generally identified by Convention rather than any strict criteria with seven regions Publishing is the process of production and dissemination of Literature or Information &ndash the activity of making information available for public view Printed versions may include a comprehensive index, tables of distances between cities, and possibly even a cross reference of important destinations. Computer software based maps provide numerous tools to aid the user, including user-adjustable scale (a. k. a "zoom") and customized search engines to locate street addresses. An address is a Code and abstract concept expressing the fixed location of a home business or other building on the earth's surface
Historically, large maps were presented (but not necessarily published, due to prohibitive labor costs) as scrolls, a famous example of which is the recently rediscovered hand-made copy of the Tabula Peutingeriana[1]. A wage is a compensation workers receive in exchange for their labor. A scroll is a roll of Papyrus, Parchment, or Paper which has been written drawn or painted upon for the purpose of transmitting information or using as The Tabula Peutingeriana ( Peutinger table) is an Itinerarium showing the Cursus publicus, the road network in the Roman Empire.
For modern examples, published maps designed for the hiker (e. The word 'hiking' is understood in all English-speaking countries but there are differences in usage g. USGS Topographic maps, a. The United States Geological Survey ( USGS) is a scientific agency of the United States government. A topographic map is a type of Map characterized by large-scale detail and quantitative representation of relief, usually using Contour lines in modern k. a. "Topos") are often scaled at the ratio of approximately 1:25,000, while maps designed for the motorist to display major highways might be scaled at 1:250,000 or 1:1,000,000. Driving is the controlled operation of a land Vehicle, usually a Motor vehicle such as a Truck or a car. * * * * * * * * * * * * * * * * * * * * * * Before adding any more images to this * * page please do carefully consider * * whether they would be mere decoration * * or actually improve In any case, a properly made map will either state its scale, or declare that it is not scaled and can not be reliably used to deduce distances.
Maps which use some quality other than physical area to determine relative size are called cartograms. A cartogram is a Map in which some thematic mapping variable – such as travel time or Gross National Product – is substituted for land area
A famous (non-cartogram) example of a map without scale is the London Underground map, which best fulfills its purpose by being less physically accurate and more visually communicative to the hurried glance of the commuter. The tube map is the Schematic diagram representing the lines stations and zones of London 's Rapid transit rail system the London Underground Commuting is the process of Travelling between one's place of residence and regular place of work This is not a cartogram (since there is no consistent measure of distance) but a topological map that also depicts approximate bearings. Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of In Navigation, a bearing is the direction one object is from another object The simple maps shown on some directional road signs are further examples of this kind. Most countries post signage known as traffic signs or road signs, at the side of Roads to
In fact, most commercial navigational maps, such as road maps and town plans, sacrifice an amount of accuracy in scale to deliver a greater visual usefulness to its user, for example by exaggerating the width of roads. Navigation is the process of reading and controlling the movement of a craft or vehicle from one place to another With the end-user similarly in mind, cartographers will censor the content of the space depicted by a map in order to provide a useful tool for that user. Economics and Commerce define an end-user as the person who uses a product. For example, a road map may or may not show railroads, smaller waterways or other prominent non-road objects, and if it does, it may show them less clearly (e. "Railroad" and "Railway" both redirect here For other uses see Railroad (disambiguation. A waterway is any navigable Body of water. These include Rivers Lakes Seas Oceans and Canals In order for a waterway g. dashed or dotted lines/outlines of various colors) than highways. * * * * * * * * * * * * * * * * * * * * * * Before adding any more images to this * * page please do carefully consider * * whether they would be mere decoration * * or actually improve Known as decluttering, the practice makes the subject matter the user is interested in easier to read, usually without sacrificing measurement accuracy. Software-based maps often allow the user to toggle decluttering between ON, OFF and AUTO as needed. In AUTO the degree of decluttering is adjusted as the user changes the scale being displayed.
Topographic maps, show elevation above (or depression below) sea level as contour lines, a specific type of Isoline. The elevation of a Geographic location is its height above a fixed reference point often the mean sea level. Mean sea level (MSL is the average (mean height of the Sea, with reference to a suitable reference surface A contour line (also Level set, isopleth, isoline, isogram or isarithm) of a function of two Isolines on any map or chart indicate the constant labeled value, such as elevation, temperature, or rainfall, for that particular line. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Rain is Liquid precipitation. On Earth it is the condensation of atmospheric Water vapor into drops heavy enough to fall often making it to Depending on the type of a map, alternative representations of elevation (or depression) exist as well.
World maps and projections
Maps of the world or large areas are often either 'political' or 'physical'. The National Oceanic and Atmospheric Administration ( NOAA) is a scientific agency within the United States Department of Commerce focused on the conditions of the The most important purpose of the political map is to show territorial borders; the purpose of the physical is to show features of geography such as mountains, soil type or land use. Geography (from Greek γεωγραφία - geografia) is the study of the Earth and its lands features inhabitants and phenomena Geological maps show not only the physical surface, but characteristics of the underlying rock, fault lines, and subsurface structures. In Geology a fault, or fault line, is a planar rock fracture which shows evidence of relative movement
Maps that depict the surface of the Earth also use a projection, a way of translating the three-dimensional real surface of the geoid to a two-dimensional picture. A map projection is any method of representing the Surface of a sphere or other shape on a plane. The geoid is that Equipotential surface which would coincide exactly with the mean ocean surface of the Earth if the oceans were in equilibrium at rest and extended through Perhaps the best-known world-map projection is the Mercator Projection, originally designed as a form of nautical chart. The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator, in 1569 A nautical chart is a graphic representation of a maritime area and adjacent Coastal regions
Airplane pilots use aeronautical charts based on a Lambert conformal conic projection, in which a cone is laid over the section of the earth to be mapped. A Lambert conformal conic projection ( LCC) is a conic Map projection, which is often used for Aeronautical charts In essence the projection The cone intersects the sphere (the earth) at one or two parallels which are chosen as standard lines. This allows the pilots to plot a great-circle route approximation on a flat, two-dimensional chart.
- Azimuthal or Gnomonic map projections are often used in planning air routes due to their ability to represent great circles as straight lines. A map projection is any method of representing the Surface of a sphere or other shape on a plane. The gnomonic Map projection displays all Great circles as straight lines A map projection is any method of representing the Surface of a sphere or other shape on a plane. A great circle is a Circle on the surface of a Sphere that has the same circumference as the sphere dividing the sphere into two equal Hemispheres. Reginald Buckminster Fuller patented one such Gnomonic projection in 1946 as the Dymaxion Map. Richard Buckminster “Bucky” Fuller ( July 12, 1895 &ndash July 1, 1983) was an American Architect, Author Year 1946 ( MCMXLVI) was a Common year starting on Tuesday (link will display full 1946 calendar of the Gregorian calendar. The Dymaxion map of the Earth is a projection of a global map onto the surface of a Polyhedron, which can then be unfolded to a net
- Richard Edes Harrison produced a striking series of maps during and after World War II for Fortune magazine. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including Fortune is a Global Business Magazine published by Time Inc's Fortune|Money Group These used "bird's eye" projections to emphasize globally strategic "fronts" in the air age, pointing out proximities and barriers not apparent on a conventional rectangular projection of the world.
Electronic maps
From the last quarter of the 20th century, the indispensable tool of the cartographer has been the computer. Much of cartography, especially at the data-gathering survey level, has been subsumed by Geographic Information Systems (GIS). The functionality of maps has been greatly advanced by technology simplifying the superimposition of spatially located variables onto existing geographical maps. Having local information such as rainfall level, distribution of wildlife, or demographic data integrated within the map allows more efficient analysis and better decision making. In the pre-electronic age such superimposition of data led Dr. John Snow to discover the cause of cholera. John Snow ( 15 March 1813 &ndash 16 June 1858) was a British physician and a leader in the adoption of Anaesthesia and medical Cholera, sometimes known as Asiatic cholera or epidemic cholera, is an infectious Gastroenteritis caused by the Bacterium Today, it is used by agencies as diverse as wildlife conservationists and militaries around the world.
Even when GIS is not involved, most cartographers now use a variety of computer graphics programs to generate new maps.
Interactive, computerised maps are commercially available, allowing users to zoom in or zoom out (respectively meaning to increase or decrease the scale), sometimes by replacing one map with another of different scale, centred where possible on the same point. In-car satellite navigation systems are computerised maps with route-planning and advice facilities which monitor the user's position with the help of satellites. Global Navigation Satellite System (GNSS is the standard generic term for satellite navigation systems that provide autonomous geo-spatial positioning with global coverage From the computer scientist's point of view, zooming in entails one or a combination of:
- replacing the map by a more detailed one
- enlarging the same map without enlarging the pixels, hence showing more detail by removing less information compared to the less detailed version
- enlarging the same map with the pixels enlarged (replaced by rectangles of pixels); no additional detail is shown, but, depending on the quality of one's vision, possibly more detail can be seen; if a computer display does not show adjacent pixels really separate, but overlapping instead (this does not apply for an LCD, but may apply for a cathode ray tube), then replacing a pixel by a rectangle of pixels does show more detail. In Digital imaging, a pixel ( pict ure el ement is the smallest piece of information in an image The cathode ray tube (CRT is a Vacuum tube containing an Electron gun (a source of electrons and a Fluorescent screen with internal or A variation of this method is interpolation. In the mathematical subfield of Numerical analysis, interpolation is a method of constructing new data points within the range of a Discrete set of
For example:
- Typically (2) applies to a Portable Document Format (PDF) file or other format based on vector graphics. The increase in detail is, of course, limited to the information contained in the file: enlargement of a curve may eventually result in a series of standard geometric figures such as straight lines, arcs of circles or splines.
- (2) may apply to text and (3) to the outline of a map feature such as a forest or building.
- (1) may apply to the text (displaying labels for more features), while (2) applies to the rest of the image. Text is not necessarily enlarged when zooming in. Similarly, a road represented by a double line may or may not become wider when one zooms in.
- The map may also have layers which are partly raster graphics and partly vector graphics. In Computer graphics, a raster graphics image or bitmap, is a Data structure representing a generally rectangular grid of Pixels Vector graphics is the use of geometrical primitives such as points lines, Curves and shapes or Polygon (s which are all based For a single raster graphics image (2) applies until the pixels in the image file correspond to the pixels of the display, thereafter (3) applies.
See also Webpage (Graphics), PDF (Layers), Mapquest, Google Maps, Google Earth or Yahoo! Maps. A web page or webpage is a resource of information that is suitable for the World Wide Web and can be accessed through a Web browser. MapQuest is a Map publisher and a free online Web mapping service owned by AOL. Google Maps (for a time named Google Local) is a free Web mapping service application and technology provided by Google that powers many map-based services Google Earth is a Virtual globe program that was originally called Earth Viewer and was created by Keyhole Inc, a company acquired by Google in 2004 Yahoo! Maps is a free online mapping portal provided by Yahoo!.
Labeling
To communicate spatial information effectively, features such as rivers, lakes, and cities need to be labeled. Cartographic labeling is a form of Typography and strongly deals with Form, style, weight and size of type on a map Over centuries cartographers have developed the art of placing names on even the densest of maps. Text placement or name placement can get mathematically very complex as the number of labels and map density increases. Therefore, text placement is time-consuming and labor-intensive, so cartographers and GIS users have developed automatic label placement to ease this process. Automatic label placement (sometimes called text placement or name placement) refers to the computer methods of placing labels automatically on a map or chart [2][3]
Footnotes
- ^ BBC NEWS | Europe | Ancient Roman road map unveiled
- ^ Imhof, E. , “Die Anordnung der Namen in der Karte,” Annuaire International de Cartographie II, Orell-Füssli Verlag, Zürich, 93-129, 1962.
- ^ Freeman, H. ,, Map data processing and the annotation problem, Proc. 3rd Scandinavian Conf. on Image Analysis, Chartwell-Bratt Ltd. Copenhagen, 1983.
References
- David Buisseret, ed. , Monarchs, Ministers and Maps: The Emergence of Cartography as a Tool of Government in Early Modern Europe. Chicago: University of Chicago Press, 1992, ISBN 0-226-07987-2
- Freeman, Herbert, Automated Cartographic Text Placement. White paper.
- Ahn, J. and Freeman, H. , “A program for automatic name placement,” Proc. AUTO-CARTO 6, Ottawa, 1983. 444-455.
- Freeman, H. , “Computer Name Placement,” ch. 29, in Geographical Information Systems, 1, D. J. Maguire, M. F. Goodchild, and D. W. Rhind, John Wiley, New York, 1991, 449-460.
- Mark Monmonier, How to Lie with Maps, ISBN 0-226-53421-9
- O'Connor, J. J. and E. F. Robertson, The History of Cartography. Scotland : St. Andrews University, 2002.
- Denis E. Cosgrove (ed. ) Mappings. Reaktion Books, 1999 ISBN 1-86189-021-4
See also
- General
- Map design and types
- Modern maps
- Censorship of maps
- Google Maps
- Japanese map symbols
- List of online map services
- MapQuest
- Maps of the UK and Ireland
- Maps of the United States
- NASA World Wind
- Map history
- Ancient world maps
- George Bradshaw, including maps of the British railway network, first published in 1839
- History of cartography
- Ordnance Survey UK map agency
- Sanborn Maps - detailed American fire insurance maps
- Related Topics
- Aerial landscape art
- Aerial photography
- Automatic label placement
- Geographic coordinate system
- Geography Cup
- Map database management
- Orthophoto
External links
- Geography and Maps, an Illustrated Guide, by the staff of the U. An atlas is a collection of Maps typically of Earth or a region of Earth but there are atlases of the other planets (and their satellites in the solar system Automatic label placement (sometimes called text placement or name placement) refers to the computer methods of placing labels automatically on a map or chart Geography (from Greek γεωγραφία - geografia) is the study of the Earth and its lands features inhabitants and phenomena A globe is a three- Dimensional scale model of Earth ( terrestrial globe) or other spheroid celestial body such as a planet star or moon A cartogram is a Map in which some thematic mapping variable – such as travel time or Gross National Product – is substituted for land area For Compass Airlines an Airline in the US using the Callsign "Compass Rose" See Compass Airlines A compass rose is a figure displaying the orientation A contour line (also Level set, isopleth, isoline, isogram or isarithm) of a function of two The Dymaxion map of the Earth is a projection of a global map onto the surface of a Polyhedron, which can then be unfolded to a net Estate maps were maps commissioned by individual landowners or institutions showing their property typically including fields and buildings A floor plan ( floorplan) in Architecture and Building engineering is a Diagram, usually to scale, of the relationships between rooms A geologic map or geological map is a special-purpose Map made to show Geological features A nautical chart is a graphic representation of a maritime area and adjacent Coastal regions Pictorial maps are a category of Maps that are also loosely called illustrated maps panoramic maps perspective maps bird’s-eye view maps and Geopictorial A planform or Plan view is a vertical Orthographic projection of an object on a horizontal plane like a Map. A plat consists of a Map, drawn to scale showing the divisions of a piece of land A reversed map, also known as an Upside-Down map or South-Up map, is a World map that generally shows Australia and New Zealand A road atlas is a Map or set of maps that primarily display Roads and transport links rather than geographical information A street map is a map showing Roads and Streets in a district or entire City. A thematic map displays spatial pattern of a theme or series of attributes A topographic map is a type of Map characterized by large-scale detail and quantitative representation of relief, usually using Contour lines in modern If you are looking for an editable blank World political map go to A world map is a Map of the surface of the Earth, which may be Censorship of maps describes the way of handling the appearance of potential strategically important objects like Military bases, Power plants or Transmitters Google Maps (for a time named Google Local) is a free Web mapping service application and technology provided by Google that powers many map-based services This is a list of symbols appearing on Japanese maps. These symbols are called in the Japanese language. Online maps can be basically divided by the covered area (global or local and by the representation of this area (classic drawn or Orthophoto) MapQuest is a Map publisher and a free online Web mapping service owned by AOL. Maps of the UK and Ireland are available in various media Maps on CD ROM ISYS OUTDOORS Anquet Maps and Fugawi offer a series of 125000 150000 WorldWind is a free Open source Virtual globe developed by NASA and open source community for use on Personal computers running Microsoft Early world maps cover depictions of the World from Classical times to the Age of Discovery and the emergence of modern Geography ( 6th century BC George Bradshaw ( July 29, 1801 - September 6, 1853) was an English Cartographer, printer and Publisher and the Cartography or mapmaking (in Greek chartis = map and graphein = write has been an integral part of the human story for a long time (maybe 8000 years Ordnance Survey (OS is an Executive agency of the United Kingdom government Sanborn Maps were originally created for assessing Fire insurance liability in urbanized areas in the United States. (This article concerns painting and other non-photographic media Aerial photography is the taking of Photographs of the ground from an elevated position Automatic label placement (sometimes called text placement or name placement) refers to the computer methods of placing labels automatically on a map or chart A geographic coordinate system enables every location on the Earth to be specified in three coordinates using mainly a spherical coordinate system. The Geography Cup is an Online, International competition between the United States and the United Kingdom, with the aim of determining Map database management stems from navigation units becoming more common in automotive vehicles (see Automotive navigation system) An orthophoto or orthophotograph is an aerial photograph that has been geometrically corrected ("orthorectified" such that the scale of the photograph S. Library of Congress. The Library of Congress is the De facto National library of the United States and the research arm of the United States Congress
- Wikipedia:Maps, use of maps on Wikipedia
- Online map collections at the Library of Congress
- Historical Maps from the Hargrett Library Collection (University of Georgia) - browse over 1000 maps from as early as 1544. ***************************************************************************************** * * The Library of Congress is the De facto National library of the United States and the research arm of the United States Congress DjVu format; requires free plugin or JAVA
Dictionary
map
-noun
- A visual representation of an area, whether real or imaginary.
- (mathematics) A function.
- (topology) A continuous function.
- A diagram of components of an item.
- The butterfly Araschnia levana.
-verb
- To create a visual representation of a territory, etc. via cartography.
- To inform someone of a particular idea.
- (mathematics, transitive) To act as a function on.
- (topology, transitive) To act as a continuous function on.
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