Closed cover
= Closed cover
{title2=$X=\bigcup_iF_i,\qquad F_i\text{ closed}$}
A closed cover of a <topological space> is a family of <closed sets> whose union is the whole space. A finite closed cover can be used in separation and antipodal arguments: in a <metric space>, vanishing distance to a closed member means actual membership. Unlike an <open cover>, a closed cover does not automatically have a partition of unity subordinate to its members.