nLab
closed cover

Definition

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.

Related concepts

• open cover

• schedule

References

• Dragan Janković, Chariklia Konstadilaki, On covering properties by regular closed sets, Mathematica Pannonica, 7/1 (1996) 97-111 (pdf)

Applications of closed covers in Čech homology is discussed in

• E. Floyd, Closed coverings in Čech homology theory (pdf)

Related discussion is also in this MO thread