Hans Hahn (September 27, 1879 - July 24, 1934) was an Austrian mathematician who made many contributions to functional analysis, topology, set theory, the calculus of variations, real analysis, and order theory. Events 489 - Odoacer attacks Theodoric at the Battle of Verona and is defeated again Year 1879 ( MDCCCLXXIX) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common Events 1132 - Battle of Nocera between Ranulf II of Alife and Roger II of Sicily. Year 1934 ( MCMXXXIV) was a Common year starting on Monday (link will display full 1934 calendar of the Gregorian calendar. Austria (Österreich ( officially the Republic of Austria (Republik Österreich For functional analysis as used in psychology see the Functional analysis (psychology article Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of Calculus of variations is a field of Mathematics that deals with functionals, as opposed to ordinary Calculus which deals with functions. Real analysis is a branch of Mathematical analysis dealing with the set of Real numbers In particular it deals with the analytic properties of real Order theory is a branch of Mathematics that studies various kinds of Binary relations that capture the intuitive notion of ordering providing a framework for saying He was a student at the Technische Hochschule in Vienna.

He also studied in Strasbourg, Munich and Göttingen. Strasbourg (Strasbourg stʁazbuʁ Alsatian: Strossburi,; Straßburg) is the capital and principal City of the Alsace région Munich (München; Minga is the capital city of Bavaria, Germany. Göttingen ( ˈgœtɪŋən, Low German: Chöttingen is a College town in Lower Saxony, Germany. He was appointed to the teaching staff in Vienna in 1905 and he became professor of mathematics there in 1921. Year 1905 ( MCMV) was a Common year starting on Sunday (link will display full calendar of the Gregorian calendar (or a Common year starting Year 1921 ( MCMXXI) was a Common year starting on Saturday (link will display full 1921 calendar of the Gregorian calendar In session 1905-06 Hahn substituted for Otto Stolz at Innsbruck. Otto Stolz ( May 3, 1842 – October 25, 1905) was an Austrian mathematician noted for his work on Mathematical analysis and Innsbruck is the capital city of the federal state of Tyrol in western Austria.

He was also actively interested in philosophy, and was part of a discussion group concerning Mach's positivism with Otto Neurath and Phillip Frank prior to the first world war. Otto Neurath (1882 - 1945 was an Austrian philosopher of science, sociologist, and political economist. Philipp Frank was a Physicist, Mathematician and also an influential Philosopher during the first half of the 20th century In 1922, he helped arrange Moritz Schlick's entry into the group, which led to the founding of the Vienna Circle, the group that was at the center of logical positivist thought in the 1920s. Moritz Schlick ( April 14, 1882 &ndash June 22, 1936) was a German philosopher and the founding father of Logical positivism The Vienna Circle (in German: der Wiener Kreis) was a group of philosophers who gathered around Moritz Schlick when he Logical positivism (later and more accurately called logical empiricism) is a school of philosophy that combines Empiricism, the idea that observational evidence is His most famous student was Kurt Gödel, whose Ph. Kurt Gödel (kʊɐ̯t ˈgøːdl̩ (April 28 1906 – January 14 1978 was an Austrian American Logician, Mathematician and Philosopher D. thesis was completed in 1929.

Hahn's contributions to mathematics include the famous Hahn-Banach theorem and (independently of Banach and Steinhaus) the uniform boundedness principle. In Mathematics, the Hahn–Banach theorem is a central tool in Functional analysis. In Mathematics, the uniform boundedness principle or Banach-Steinhaus theorem is one of the fundamental results in Functional analysis. Other theorems include:

• the Hahn decomposition theorem;
• the Hahn embedding theorem;
• the Hahn-Kolmogorov theorem;
• the Hahn-Mazurkiewicz theorem;
• the Vitali-Hahn-Saks theorem. In Mathematics, the Hahn decomposition theorem, named after the Austrian Mathematician Hans Hahn, states that given a measurable space In Mathematics, the Hahn embedding theorem states that every totally ordered abelian group can be embedded as a subgroup of the additive group of a Real closed Space-filling curves or Peano curves are Curves first described by Giuseppe Peano (1858–1932 whose ranges contain the entire 2-dimensional Unit In Mathematics, the Vitali–Hahn–Saks theorem states that given &mun for each integer n >0 a Countably additive function defined on a fixed

External links

• O'Connor, John J. & Robertson, Edmund F. , “Hans Hahn”, MacTutor History of Mathematics archive 
• Hans Hahn at the Mathematics Genealogy Project