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The simplicial complex formed from a family of objects by taking sets that have nonempty intersections.

The type of homology which results when the spaces being studied are restricted to simplicial complexes and subcomplexes.

The general type of homology which is what mathematicians generally mean when they say "homology." Singular homology is a more general version than Poincaré's original ...

The continuous image of a Polish space, also called an analytic set.

An abstract simplicial complex is a collection S of finite nonempty sets such that if A is an element of S, then so is every nonempty subset of A (Munkres 1993, p. 15).

Characteristic classes are cohomology classes in the base space of a vector bundle, defined through obstruction theory, which are (perhaps partial) obstructions to the ...

A homology class in a singular homology theory is represented by a finite linear combination of geometric subobjects with zero boundary. Such a linear combination is ...

The branch of algebraic topology which deals with homotopy groups. Homotopy methods can be used to solve systems of polynomials by embedding the polynomials in a family of ...

A simplicial complex K is said to be locally finite if each vertex of K belongs only to finitely many simplices of K.

Let f:K^((0))->L^((0)) be a bijective correspondence such that the vertices v_0, ..., v_n of K span a simplex of K iff f(v_0), ..., f(v_n) span a simplex of L. Then the ...