Topology/Relative Homology

Let the notation $$C_\bullet(X)$$ represent the singular chains for X then, for a subspace $$A\subset X$$ there exists a short exact sequence


 * $$0\to C_\bullet(A) \to C_\bullet(X)\to C_\bullet(X) /C_\bullet(A) \to 0$$

meaning we can define the relative homology as $$H_n(X/A)\cong H_n(C_\bullet(X)/C_\bullet(A))$$.