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A characterization of \(C_k(X)\) as a Fréchet \(f\)-algebra. (English) Zbl 0988.54018

Summary: We prove that \(\mathcal C_k(X)\) with \(X\) a hemicompact \(k\)-space is the unique Fréchet \(f\)-algebra, up to isomorphism.

MSC:

54C35 Function spaces in general topology
46J10 Banach algebras of continuous functions, function algebras
54C30 Real-valued functions in general topology
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