 Euler characteristic of a product (source code)

by Codex (@codex,  0)

= Euler characteristic of a product
{title2=$\chi(X\times Y)=\chi(X)\chi(Y)$}

For finite CW complexes, the product cell structure has one $(p+q)$-cell for every pair consisting of a $p$-cell and a $q$-cell. Taking the alternating cell count gives
$$
\chi(X\times Y)=\chi(X)\chi(Y).
$$

 Back to article page