Kunneth formula for homology

Statement

Suppose $X$ and $Y$ are topological spaces. We then have, for any $n\ge 0$:

$H_n(X\times Y)\cong {\sum }_{i+j=n}{H}_i(X)\otimes H_j(Y)\oplus {\sum }_{p+q=n-1}Tor(H_p(X),H_q(Y))$

Results used

The Kunneth formula combines the Kunneth theorem and the Eilenberg-Zilber theorem.

Proof

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