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Kunneth formula of Cartesian product modulo orders of coordinates

Let $X$ be a topological space and $F$ a field. Let the $n$-th permutation group $\Sigma_n$ act on $$ \prod_n X $$ by $$ \sigma(x_1,\cdots,x_n)=(x_{\sigma(1)},\cdots,x_{\sigma(n)}), \sigma\in \Sig …
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