Completeness properties of function spaces
The authors study function spaces \(C_ k(X)\) of all continuous real functions on a Tikhonov space X equipped with the compact-open topology. Their main interest lies in completeness properties of such spaces. A study of completeness properties of function spaces \(C_ p(X)\) equipped with the topology of pointwise convergency has been done earlier by \textit{D. Lutzer} and the first author [Pac. J. Math. 90, 145-168 (1980; Zbl 0481.54017)]. Usually, the results proven here give characterizations of properties on a space \(C_ k(X)\) in terms of properties of the space X. For example, almost \(\sigma\)-compactness of X is equivalent to submetrizability of \(C_ k(X)\) or that \(C_ k(X)\) has a \(G_{\delta}\)-diagonal; to be a hemicompact k-space for X is equivalent to complete metrizability of \(C_ k(X)\) or its Čech-completeness. Some study is also done by means of topological games.
scientific article; zbMATH DE number 4007217
scientific article