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 $H_n(X/A)\cong H_n(C_{\bullet }(X)/C_{\bullet }(A))$.

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