Open Subcover

Last updated Nov 1, 2022

Let $X$ be a Topological Space, $I \preccurlyeq \mathcal{P}(X)$ be an Index Set, $S \subset X$, and $\mathcal{U} := {U_\alpha}_{\alpha \in I}$ an Open Cover of $S$. Then $\mathcal{V} \subset \mathcal{U}$ is an Open Subcover of $S$ if it is also an Open Cover of $S$.