Bounded resolutions for spaces Cp(X) and a characterization in terms of X

0541712 - MÚ 2022 RIV ES eng J - Journal Article
Ferrando, J.C. - Kąkol, Jerzy - Śliwa, W.
Bounded resolutions for spaces Cp(X) and a characterization in terms of X.
Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Roč. 115, č. 2 (2021), č. článku 90. ISSN 1578-7303. E-ISSN 1579-1505
R&D Projects: GA ČR(CZ) GF20-22230L
Institutional support: RVO:67985840
Keywords : cosmic space * K-analytic-framed space * nice framing
OECD category: Pure mathematics
Impact factor: 2.276, year: 2021
Method of publishing: Open access
https://doi.org/10.1007/s13398-021-01029-z

An internal characterization of the Arkhangel’skiĭ-Calbrix main theorem from [4] is obtained by showing that the space Cp(X) of continuous real-valued functions on a Tychonoff space X is K-analytic framed in RX 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.
Permanent Link: http://hdl.handle.net/11104/0319242