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Fréchet Space (Functional Analysis)**

A Fréchet space is a topological vector space \((V,\mathcal{T},+,\cdot)\) such that the topological space \((V,\mathcal{T})\) is metrizable (and so also Hausdorff), \(V\) is Cauchy complete with respect to this metric, and \(V\) is locally convex.