Refinement of a cover

Let \(X\) be a topological space and let \(\mathcal U\) and \(\mathcal V\) be covers of \(X\). The cover \(\mathcal V\) is a refinement of \(\mathcal U\) if for every \(V\in\mathcal V\) there exists \(U\in\mathcal U\) with \(V\subseteq U\).