Talk:Good cover (algebraic topology)

Good covers in algebraic geometry
It should be noted on this page that the good cover on $$\mathbb{P}^n$$ induces a good cover on projective varieties embedded in it via restriction. Also, it should be noted that products of spaces with good covers produce good covers. I.e. if

(X, \mathcal{U}) \text{ } (Y,\mathcal{V}) $$ are pairs of a space with a good cover, then

(X\times Y, \mathcal{U}\times\mathcal{V}) $$ is a good cover where

\mathcal{U}\times\mathcal{V} = (U_i\times V_j)_{i \in I, j \in J} $$