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

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Trudy Instituta Matematiki i Mekhaniki 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. Osipov^ab

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

Full-text PDF (278 kB) Citations (4)

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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.

Received: 12.05.2011

Bibliographic databases:

Document Type: Article

UDC: 517.982.272+515.122.55

Language: Russian

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{https://elibrary.ru/item.asp?id=17870442}

Linking options:

https://www.mathnet.ru/eng/timm769

https://www.mathnet.ru/eng/timm/v17/i4/p258

This publication is cited in the following 4 articles:

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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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