Cellular homology

For a topological space
The cellular homology corresponding to a cellular filtration of a topological space is the homology of the corresponding defining ingredient::cellular chain complex.

The cellular homology groups coincide with the singular homology groups of the underlying topological space, and do not depend upon the cellular filtration. However, cellular homology is often easier to compute in practice for easy cellular filtrations, since the cellular chain groups are much more likely to be finite-dimensional (and often trivial) than the singular chain groups.