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.

Bing's dogbone space is an example with M (equal to R3) not homeomorphic to M/G.

for which: A cell complex is a pair