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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of $\sigma $-compactness
of a cosmic space $X$
by means of subspaces of $R^{X}$


Authors: A. V. Arhangel'skii and J. Calbrix
Journal: Proc. Amer. Math. Soc. 127 (1999), 2497-2504
MSC (1991): Primary 54C35; Secondary 54D45, 28A05.
Published electronically: April 15, 1999
MathSciNet review: 1487355
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

A. V. Arhangel'skii
Affiliation: January–June: Department of Mathematics, Ohio University, Athens, Ohio 45701; July–December: Department of Mathematics, Moscow State University, Moscow 119 899, Russia
Email: arhangel@bing.math.ohiou.edu

J. Calbrix
Affiliation: Université de Rouen, URA CNRS 1378, UFR de Sciences, 76821 Mont Saint Aignan Cedex, France
Email: Jean.Calbrix@univ-rouen.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04782-6
PII: S 0002-9939(99)04782-6
Keywords: Function spaces, topology of pointwise convergence, $\sigma $-compactness, $K$-analytic spaces
Received by editor(s): December 8, 1996
Received by editor(s) in revised form: November 1, 1997, and November 12, 1997
Published electronically: April 15, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society