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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 3, Pages 251–260 (Mi timm983)  

This article is cited in 1 scientific paper (total in 1 paper)

On the $\sigma$-countable compactness of spaces of continuous functions with the set-open topology

A. V. Osipovab, E. G. Pytkeevab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University named after B. N. Yeltsin
Full-text PDF (192 kB) Citations (1)
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Abstract: For a Tychonoff space $X$, we obtain a criterion of the $\sigma$-countable compactness of the space of continuous real-valued functions $C(X)$ with the set-open topology. In particular, for extremally disconnected space $X$, we prove that the space $C_\lambda(X)$ is a $\sigma$-countably compact space if and only if $X$ is a pseudocompact space, the set $X(P)$ of all $P$-points of $X$ is dense in $X$, and the family $\lambda$ consists of finite subsets of $X(P)$.
Keywords: set-open topology, $\sigma$-countably compact space, extremally disconnected space, $P$-point, space of continuous functions.
Received: 13.01.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2014, Volume 285, Issue 1, Pages S153–S162
DOI: https://doi.org/10.1134/S0081543814050174
Bibliographic databases:
Document Type: Article
UDC: 517.982.272+515.122.55
Language: Russian
Citation: A. V. Osipov, E. G. Pytkeev, “On the $\sigma$-countable compactness of spaces of continuous functions with the set-open topology”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 3, 2013, 251–260; Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S153–S162
Citation in format AMSBIB
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\by A.~V.~Osipov, E.~G.~Pytkeev
\paper On the $\sigma$-countable compactness of spaces of continuous functions with the set-open topology
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2013
\vol 19
\issue 3
\pages 251--260
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\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2014
\vol 285
\issue , suppl. 1
\pages S153--S162
\crossref{https://doi.org/10.1134/S0081543814050174}
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  • https://www.mathnet.ru/eng/timm/v19/i3/p251
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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    References:60
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