Abstract
AbstractAn internal characterization of the Arkhangel’skiĭ-Calbrix main theorem from [4] is obtained by showing that the space $$C_{p}(X)$$
C
p
(
X
)
of continuous real-valued functions on a Tychonoff space X is K-analytic framed in $$\mathbb {R}^{X}$$
R
X
if and only if X admits a nice framing. This applies to show that a metrizable (or cosmic) space X is $$\sigma $$
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 $$\sigma $$
σ
-boundedness of X is shown.
Funder
Ministerio de Ciencia, Innovación y Universidades
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis
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