Form equivalence class Howard-Rubin Number: 14
Statement: The Ascoli Theorem. If \(X\) is a locally compactHausdorff space, \(Y\) is a metric space, \(C_\infty(X,Y)\) is the spaceof all continuous functions from \(X\) to \(Y\) with the compact-opentopology, and \(F\) is a subspace of \(C_\infty(X,Y)\) then the followingconditions are equivalent:\itemitem{(1)} \(F\) is compact\itemitem{(2)} (a) For each \(x\in X\), the set \(F(x) =\{f(x): f\in F\}\)is compact in \(Y\).\itemitem{}(b) \(F\) is closed in the product space \(Y^X\),\itemitem{}(c) \(F\) is equicontinuous.\par Herrlich [1997b] and Note 10.
Howard-Rubin number: 14 CU
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