Long exact sequence of homology of a pair

This article defines a long exact sequence of homology groups, for topological spaces or pairs of topological spaces

Definition

Let $X$ be a topological space and $A$ a subspace. The long exact sequence of homology of the pair $(X,A)$ looks like:

$\dots H_n(A)\to H_n(X)\to H_n(X,A)\to H_{n-1}(A)\to \dots$

It is a special case of the long exact sequence of homology of a triple.