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Open Cover**

Given a topological space \((X,\mathcal{T})\) and a subset \(A\subseteq X\), an open cover of \(A\) is a collection of open sets whose union contains \(A\), i.e. \(\{U_i\}_{i\in I}\subseteq \mathcal{T}:\cup_{i\in I}U_i\supseteq A\).