A closed cover of a topological space$X$ is a collection $\{U_i \subset X\}$ of closed subsets of $X$ whose union equals $X$: $\cup_i U_i = X$. Usually it is also required that every point $x \in X$ is in the interior of one of the $U_i$.

Properties

Closed covers can be obtained from open covers by forming the closure of each of the open subsets. The result clearly satisfies the clause that every point is in the interior of one of the closed subsets.

Vladimir Berkovich, Non-archimedean analytic spaces, lectures at the Advanced School on $p$-adic Analysis and Applications, ICTP, Trieste, 31 August - 11 September 2009 (pdf)

Revised on July 17, 2014 14:44:38
by Urs Schreiber
(82.136.246.44)