Editing Excision theorem (section)

{{Short description|Theorem in algebraic topology}}

In [[algebraic topology]], a branch of [[mathematics]], the '''excision theorem''' is a theorem about [[relative homology]] and one of the [[Eilenberg–Steenrod axioms]]. Given a topological space <math>X</math> and subspaces <math>A</math> and <math>U</math> such that <math>U</math> is also a subspace of <math>A</math>, the theorem says that under certain circumstances, we can cut out ('''excise''') <math>U</math> from both spaces such that the [[Relative_homology|relative homologies]] of the pairs <math>(X \setminus U,A \setminus U )</math> into <math>(X, A)</math> are isomorphic.

This assists in computation of [[singular homology]] groups, as sometimes after excising an appropriately chosen subspace we obtain something easier to compute.