Let X be a topological space and let y be a point in X. Denote H'_n(X) be the reduced homology of X and Denote H_n(X,y) the relative homology of X and the one point space {y}.(adsbygoogle = window.adsbygoogle || []).push({});

Prove: H'_n(X) is isomorphic to H_n(X,y).

I have proven that it is true for n>0. But, for n=0, I get H_n(X) isomorphic to H_n(X,y) and since the reduced homology of X is H_n(X) mod integers, I have run into a contradiction. Wikipedia gives my result as a property of relative homology, but my teacher has something different. (Note H_n(X)=H'_n(X) for n>0).

Help?!??!

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# Relative Singular Homology

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