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A characterization of
Authors:A V Arhangel'skii  J Calbrix
Institution:January--June: Department of Mathematics, Ohio University, Athens, Ohio 45701 - July--December: Department of Mathematics, Moscow State University, Moscow 119 899, Russia ; Université de Rouen, URA CNRS 1378, UFR de Sciences, 76821 Mont Saint Aignan Cedex, France
Abstract:This work is devoted to the relationship between topological properties of a space $X$ and those of $C_{p}(X)$ (= the space of continuous real-valued functions on $X$, with the topology of pointwise convergence). The emphasis is on $\sigma $-compactness of $X$ and on location of $C_{p}(X)$ in $R^{X}$. In particular, $\sigma $-compact cosmic spaces are characterized in this way.

Keywords:Function spaces  topology of pointwise convergence  $\sigma $-compactness  $K$-analytic spaces
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