In mathematics, a closed n-manifold embedded in an (n + 1)-manifold is boundary parallel (or ∂-parallel, or peripheral) if it can be isotoped onto a boundary component. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Closed may refer to Math Closure (mathematics Closed manifold Closed orbits Closed A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be In Mathematics, an embedding (or imbedding) is one instance of some Mathematical structure contained within another instance such as a group In Topology, two continuous functions from one Topological space to another are called homotopic ( Greek homos = identical For a different notion of boundary related to Manifolds see that article In Topology and related branches of Mathematics, a connected space is a Topological space which cannot be represented as the disjoint union of

An example

Consider the annulus . Let π denote the projection map

If a circle S is embedded into the annulus so that π restricted to S is a bijection, then S is boundary parallel. In Mathematics, a bijection, or a bijective function is a function f from a set X to a set Y with the property (The converse is not true. Conversion is a concept in Traditional logic referring to a "type of immediate Inference in which from a given Proposition another proposition is inferred )

If, on the other hand, a circle S is embedded into the annulus so that π restricted to S is not surjective, then S is not boundary parallel. In Mathematics, a function f is said to be surjective or onto, if its values span its whole Codomain; that is for every (Again, the converse is not true. )

An example wherein π is not bijective on S, but S is ∂-parallel anyway.

An example wherein π is bijective on S.

An example wherein π is not surjective on S.