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Title: A note on condensations of $C_p(X)$ onto compacta (English)
Author: Arhangel'skii, A. V.
Author: Pavlov, O. I.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 43
Issue: 3
Year: 2002
Pages: 485-492
Category: math
Summary: A condensation is a one-to-one continuous mapping onto. It is shown that the space $C_p(X)$ of real-valued continuous functions on $X$ in the topology of pointwise convergence very often cannot be condensed onto a compact Hausdorff space. In particular, this is so for any non-metrizable Eberlein compactum $X$ (Theorem 19). However, there exists a non-metrizable compactum $X$ such that $C_p(X)$ condenses onto a metrizable compactum (Theorem 10). Several curious open problems are formulated. (English)
Keyword: condensation
Keyword: compactum
Keyword: network
Keyword: Lindelöf space
Keyword: topology of pointwise convergence
Keyword: $\sigma $-compact space
Keyword: Eberlein compactum
Keyword: Corson compactum
Keyword: Borel set
Keyword: monolithic space
Keyword: tightness
MSC: 54A25
MSC: 54A35
MSC: 54C35
MSC: 54D30
idZBL: Zbl 1090.54003
idMR: MR1920523
Date available: 2009-01-08T19:24:06Z
Last updated: 2012-04-30
Stable URL:
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