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Closed Set**

Given a topological space \((X,\mathcal{T})\), a subset \(A\subseteq X\) is 'closed' (with respect to the topology \(\mathcal{T}\)) if its complement is open, i.e. \(X\backslash A\in\mathcal{T}\). The definition of a topology means that \(\emptyset\) and \(X\) are always closed, as is the union of a finite number of closed sets and the intersection of an arbitrary number of closed sets.