Bounded resolutions for spaces C_{p}(X) and a characterization in terms of X

Abstract

An internal characterization of the Arkhangel’skiĭ-Calbrix main theorem from [4] is obtained by showing that the space C_{p}(X) of continuous real-valued functions on a Tychonoff space X is K-analytic framed in mathbb {R}^{X} if and only if X admits a nice framing. This applies to show that a metrizable (or cosmic) space X is sigma -compact if and only if X has a nice framing. We analyse a few concepts which are useful while studying nice framings. For example, a class of Tychonoff spaces X containing strictly Lindelöf Čech-complete spaces is introduced for which a variant of Arkhangel’skiĭ-Calbrix theorem for sigma -boundedness of X is shown.