Cellular decomposition

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 R³) not homeomorphic to M/G.

See also

• CW complex

References

• Daverman, Robert J. (2007), Decompositions of manifolds, AMS Chelsea Publishing, Providence, RI, p. 22, ISBN 978-0-8218-4372-7, MR 2341468