Cellular decomposition
Introduction In geometric topology, a '''cellular decomposition''' ''G'' of a manifold ''M'' is a decomposition of ''M'' as the disjoint union of cells (spaces homeomorphic to ''n''-balls ''Bn'').The quotient space ''M''/''G'' has points that correspond to the cells of the decomposition. There is a natural map from ''M'' to ''M''/''G'', which is given the quotient topology. A fundamental question is whether ''M'' is homeomorphic to ''M''/''G''. Bing's dogbone space is an example with ''M'' (equal to '''R'''3) not homeomorphic to ''M''/''G''.
Definition Cellular decomposition of  is an open cover  with a function  for which:* Cells are disjoint: for any distinct , . * No set gets mapped to a negative number: . * Cells look like balls: For any  and for any  there exists a continuous map  that is an isomorphism  and also .A cell complex is a pair  where  is a topological space and  is a cellular decomposition of .
See also *CW complex
References *