Ferrando, J.C., Ka̧kol, J., Śliwa, W. (2021) «Bounded resolutions for spaces Cp(X) and a characterization in terms of X», Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales – Serie A: Matematicas, 115 (2):90

Juan Carlos Ferrando (Operations Research Center, University Miguel Hernández of Elche), Jerzy Kąkol (Faculty of Mathematics and Informatics, A. Mickiewicz University, Poznań) and Wiesław Śliwa (Institute of Mathematics, College of Natural Sciences, University of Rzeszów)

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 R^X if and only if X admits a nice framing. This applies to show that a metrizable (or cosmic) space X is σ -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 σ-boundedness of X is shown.