CW complex

In topology, a CW complex is a type of topological space introduced by J.H.C. Whitehead to meet the needs of homotopy theory. The idea was to have a class of spaces that was broader than simplicial complexes (we could say now, had better categorical properties); but still retained a combinatorial nature, so that computational considerations were not ignored. The name itself is unrevealing: CW stands for closure-finite weak topology.

Related Topics:
Topology - Topological space - J.H.C. Whitehead - Homotopy theory - Simplicial complex - Categorical

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For these purposes a closed cell is a topological space homeomorphic to a simplex, or equally a ball (sphere plus interior) or cube in n dimensions. Only the topological nature matters: but one does want to keep track of the subspace on the 'surface' (the sphere that bounds the ball), and its complement, the interior points. A general cell complex would be a topological space X that is covered by cells; or to put it another way, we start with a space that is the disjoint union of some collection of cells, and take X as a quotient space, for some equivalence relation. This is too general a concept.

Related Topics:
Simplex - Quotient space

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