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Metrizable**

A topological space \((X,\mathcal{T})\) is called metrizable if the topology arises from a metric, i.e. if there exists a function \(d:X\times X\to \mathbb{R}_{\geq0}\) such that \((X,d)\) is a metric space, and \(\mathcal{T}\) is equal to the induced topology on \(X\) due to \(d\).