Function spaces homeomorphic to the countable product of \(\ell ^ f_ 2\)
Let \(C_ p(X)\) denote the space of continuous real-valued functions defined on a topological space X endowed with the pointwise convergence topology. Let \(C^*_ p(X)\) denote the linear subspace of \(C_ p(X)\) consisting of bounded functions. Let \(\ell^ f_ 2\) denote the subspace of the Hilbert space \(\ell^ 2\) consisting of all sequences for which all but finitely many terms are zero. The following is the main result of the paper: If X is a nondiscrete countable metric space, then each of \(C_ p(X)\) and \(C^*_ p(X)\) is homeomorphic to the countable infinite product \(\ell^ f_ 2\times \ell^ f_ 2\times... \).
space of continuous real-valued functions
scientific article; zbMATH DE number 4131277
scientific article