Abstract:
The 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.
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
\Bibitem{NokOsi09}
\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{https://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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000274041900016}
Linking options:
https://www.mathnet.ru/eng/timm233
https://www.mathnet.ru/eng/timm/v15/i2/p177
This publication is cited in the following 13 articles:
Mikhail Al'perin, Sergei Nokhrin, Alexander V. Osipov, “Embedding theorems for function spaces”, Topology and its Applications, 332 (2023), 108523
Tarun Kumar Chauhan, Varun Jindal, “CLOPEN LINEAR SUBSPACES AND CONNECTEDNESS IN FUNCTION SPACES”, Rocky Mountain J. Math., 53:5 (2023)
J.A. Martínez-Cadena, Á. Tamariz-Mascarúa, “The topology of uniform convergence on Lindelöf subsets”, Topology and its Applications, 311 (2022), 107960
Juan Alberto Martínez-Cadena, Ángel Tamariz-Mascarúa, “The Selectively Pseudocompact-Open Topology on C(X)”, Bull. Iran. Math. Soc., 47:5 (2021), 1611
Alexander V. Osipov, “Indestructibly productively Lindelöf and Menger function spaces”, Topology and its Applications, 281 (2020), 107202
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
Alqurashi W.Kh., Khan L.A., Osipov A.V., “Set-Open Topologies on Function Spaces”, Appl. Gen. Topol., 19:1 (2018), 55–64
Alqurashi W.Kh., Khan L.A., “Quasi-Uniform Convergence Topologies on Function Spaces - Revisited”, Appl. Gen. Topol., 18:2 (2017), 301–316
A. Bouchair, S. Kelaiaia, “Comparison of some set open topologies on C(X,Y)”, Topology and its Applications, 178 (2014), 352
Osipov A.V., “Topological-algebraic properties of function spaces with set-open topologies”, Topology Appl, 159:3 (2012), 800–805
A. V. Osipov, “O svoistvakh tipa polnoty $C$-kompaktno-otkrytoi topologii na $C(X)$”, Tr. IMM UrO RAN, 18, no. 2, 2012, 191–198
A. V. Osipov, “Svoistva $C$-kompaktno-otkrytoi topologii na prostranstve funktsii”, Tr. IMM UrO RAN, 17, no. 4, 2011, 258–277
A. V. Osipov, “Slabo mnozhestvenno-otkrytaya topologiya”, Tr. IMM UrO RAN, 16, no. 2, 2010, 167–176
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