Excision Axiom

One of the Eilenberg-Steenrod Axioms which states that, if $X$ is a Space with Subspaces $A$ and $U$ such that the Closure of $A$ is contained in the interior of $U$, then the Inclusion Map $(X \ U, A \ U) \to (X,A)$ induces an isomorphism $H_n(X \ U, A \ U) \to H_n(X,A)$.