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

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