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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 2, Pages 177–184 (Mi timm233)  

This article is cited in 7 scientific papers (total in 7 papers)

On the coincidence of the set-open and uniform topologies

S. È. Nokhrin, A. V. Osipova

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

Abstract: The $\mathbb R$-compactness property is studied and criteria are established for the coincidence of the set-open topology and the topology of uniform convergence on the spaces of continuous functions.

Keywords: space of continuous functions, set-open topology, topology of uniform convergence on a family of sets

Full text: PDF file (168 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 267, suppl. 1, S184–S191

Bibliographic databases:

UDC: 517.982.272+515.122.55
Received: 03.02.2009

Citation: S. È. Nokhrin, A. V. Osipov, “On the coincidence of the set-open and uniform topologies”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 177–184; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S184–S191

Citation in format AMSBIB
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\by S.~\`E.~Nokhrin, A.~V.~Osipov
\paper On the coincidence of the set-open and uniform topologies
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 2
\pages 177--184
\mathnet{http://mi.mathnet.ru/timm233}
\elib{http://elibrary.ru/item.asp?id=12878779}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 267
\issue , suppl. 1
\pages S184--S191
\crossref{https://doi.org/10.1134/S0081543809070165}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000274041900016}


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

    This publication is cited in the following articles:
    1. A. V. Osipov, “Slabo mnozhestvenno-otkrytaya topologiya”, Tr. IMM UrO RAN, 16, no. 2, 2010, 167–176  mathnet  elib
    2. A. V. Osipov, “Svoistva $C$-kompaktno-otkrytoi topologii na prostranstve funktsii”, Tr. IMM UrO RAN, 17, no. 4, 2011, 258–277  mathnet  elib
    3. Osipov A.V., “Topological-algebraic properties of function spaces with set-open topologies”, Topology Appl, 159:3 (2012), 800–805  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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
    5. Alqurashi W.Kh., Khan L.A., “Quasi-Uniform Convergence Topologies on Function Spaces - Revisited”, Appl. Gen. Topol., 18:2 (2017), 301–316  crossref  mathscinet  isi  scopus
    6. Alqurashi W.Kh., Khan L.A., Osipov A.V., “Set-Open Topologies on Function Spaces”, Appl. Gen. Topol., 19:1 (2018), 55–64  crossref  mathscinet  zmath  isi  scopus
    7. Harkat L., Bouchair A., Kelaiaia S., “Comparison of Some Set Open and Uniform Topologies and Some Properties of the Restriction Maps”, Hacet. J. Math. Stat., 48:1 (2019), 17–27  crossref  isi
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