One of the Eilenberg-Steenrod axioms. It states that, for every pair (X, A), there is a natural long exact sequence ...->H_n(A)->H_n(X)->H_n(X, A)->H_(n - 1)(A)->..., where the map H_n(A)->H_n(X) is induced by the inclusion map A->X and H_n(X)->H_n(X, A) is induced by the inclusion map (X, ϕ)->(X, A). The map H_n(X, A)->H_(n - 1)(A) is called the boundary map.

Eilenberg-Steenrod axioms | long exact sequence