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Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 4, Pages 258–277 (Mi timm769)  

This article is cited in 4 scientific papers (total in 4 papers)

Properties of the $C$-compact-open topology on a function space

A. V. Osipovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University

Abstract: We study the $C$-compact-open topology on the set $C(X)$ of all continuous real-valued functions defined on a Tikhonov space $X$. The relations between the $C$-compact-open topology and the compact-open and bounded-open topologies on the set $X$ are studied. We also investigate the cardinal-valued characteristics of the space $C(X)$ equipped with the $C$-compact-open topology, for example, the Suslin number, Lindelöf number, weight, and density.

Keywords: space of continuous functions, set-open topology, compact-open topology, $C$-compact subset, topology of uniform convergence.

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UDC: 517.982.272+515.122.55
Received: 12.05.2011

Citation: A. V. Osipov, “Properties of the $C$-compact-open topology on a function space”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 4, 2011, 258–277

Citation in format AMSBIB
\Bibitem{Osi11}
\by A.~V.~Osipov
\paper Properties of the $C$-compact-open topology on a~function space
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 4
\pages 258--277
\mathnet{http://mi.mathnet.ru/timm769}
\elib{http://elibrary.ru/item.asp?id=17870442}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Osipov, “Sopryazhennoe prostranstvo k $C_{rc}(X)$”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 1, 41–49  mathnet
    2. A. V. Osipov, “O svoistvakh tipa polnoty $C$-kompaktno-otkrytoi topologii na $C(X)$”, Tr. IMM UrO RAN, 18, no. 2, 2012, 191–198  mathnet  elib
    3. Alexander V. Osipov, “On the completeness properties of the $C$-compact-open topology on $C(X)$”, Ural Math. J., 1:1 (2015), 61–67  mathnet  crossref  zmath
    4. A. V. Osipov, “Razlichnye vidy tesnoty funktsionalnogo prostranstva”, Tr. IMM UrO RAN, 22, no. 3, 2016, 192–199  mathnet  crossref  mathscinet  elib
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