Editing Excision theorem (section)

=== Statement === 
If <math>U\subseteq A \subseteq X</math> are as above, we say that <math>U</math> can be '''excised''' if the inclusion map of the pair <math>(X \setminus U,A \setminus U )</math> into <math>(X, A)</math> induces an isomorphism on the relative homologies: 

{{center|<math>H_n(X \setminus U,A \setminus U) \cong H_n(X,A)</math>}}

The theorem states that if the [[Closure (topology)|closure]]  of <math>U</math> is contained in the [[Interior (topology)|interior]] of <math>A</math>, then <math>U</math> can be excised.

Often, subspaces that do not satisfy this containment criterion still can be excised&mdash;it suffices to be able to find a [[deformation retract]] of the subspaces onto subspaces that do satisfy it.