Cellular decomposition
In geometric topology, a cellular decomposition G of a manifold M is a decomposition of M as the disjoint union of cells.
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'' 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.