Cellular homology

Definition

For a topological space

The cellular homology corresponding to a cellular filtration of a topological space is the homology of the corresponding 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.

For a pair of topological spaces

Fill this in later