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The map H_n(X,A)->H_(n-1)(A) appearing in the long exact sequence of a pair axiom.

A topological space.

That portion of a region lying "outside" a specified boundary.

A field of extremals is a plane region which is simply connected by a one-parameter family of extremals. The concept was invented by Weierstrass.

A property of a space which is also true of each of its subspaces. Being "first-countable" is hereditary, but having a given genus is not.

An open connected set is called a region (sometimes also called a domain).

The set closure St^_v of a star Stv at a vertex v of a simplicial complex K.

If the abstract simplicial complex S is isomorphic with the vertex scheme of the simplicial complex K, then K is said to be a geometric realization of S, and is uniquely ...

A half-space is that portion of an n-dimensional space obtained by removing that part lying on one side of an (n-1)-dimensional hyperplane. For example, half a Euclidean ...

The following three pieces of information completely determine the homeomorphic type of a surface (Massey 1996): 1. Orientability, 2. Number of boundary components, 3. Euler ...