# Homological codimension of a subspace

From Topospaces

*This term is nonstandard and is being used locally within the wiki. For its use outside the wiki, please define the term when using it.*

## Definition

Let be a topological space and a subspace. is said to have *homological codimension* in if is nonempty, and for every point , there exists a neighbourhood of such that:

and all other homologies are 0.

## Facts

If is a manifold and is a closed subset which is also a tame submanifold, then has cohomological dimension in equal to the difference of dimensions of and .