Let \(X\) be a set and \(\mathcal U = \ts{U_\alpha}_{\alpha\in I}\) a collection of subsets of \(X\). The collection \(\mathcal U\) is a cover of \(X\) if \(X = \Union_{\alpha\in I} U_\alpha\), and a cover of a subset \(A\subseteq X\) if \(A\subseteq \Union_{\alpha\in I} U_\alpha\). If \(X\) is a topological space and every \(U_\alpha\) is open, \(\mathcal U\) is an open cover.
Cover of a space or subset
D-AOJG3