Covers#

Definition: Cover

Let \(X\) be a set.

A collection \(\mathcal{C}\) of subsets of \(X\) is a cover of \(X\) if \(X\) is a subset of the union of \(\mathcal{C}\).

Definition: Subcover

Let \(X\) be a set and let \(\mathcal{C}\) be a cover of \(X\).

A subcover of \(\mathcal{C}\) is subcollection of \(\mathcal{C}\) which is still a cover of \(X\).