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Izvestiya: Mathematics, 2016, Volume 80, Issue 2, Pages 442–461
DOI: https://doi.org/10.1070/IM8348 (Mi im8348) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Local and global continuous $\varepsilon$-selection

I. G. Tsar'kov

M. V. Lomonosov Moscow State University
English version PDF (316 kB) Citations (21) Russian version article
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DOI: https://doi.org/10.1070/IM8348
Abstract: We study properties of sets for which there is a continuous selection from the set of almost-best approximants. We establish relations between local and global selections, give various examples of sets possessing a continuous $\varepsilon$-selection, and introduce the notions of moduli of approximative continuity, approximative $\delta$-solarity and uniform approximative continuity. These notions enable us to establish the $\delta$-solarity of sets under certain conditions.
Keywords: $\varepsilon$-selection, monotone path-connected sets, $\delta$-solarity, $\mathring{B}$-infinite connectedness, $\mathring{B}$-approximative infinite connectedness, moduli of approximative continuity.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00022-a
This paper was written with the support of the Russian Foundation for Basic Research (grant no. 13-01-00022-a).
Received: 01.02.2015
Revised: 03.06.2015
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
MSC: 46B20, 54C65, 41A65
Language: English
Original paper language: Russian
Citation: I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461
Citation in format AMSBIB
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\by I.~G.~Tsar'kov
\paper Local and global continuous $\varepsilon$-selection
\jour Izv. Math.
\yr 2016
\vol 80
\issue 2
\pages 442--461
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    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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