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Sbornik: Mathematics, 2016, Volume 207, Issue 2, Pages 267–285
DOI: https://doi.org/10.1070/SM8481 (Mi sm8481) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Continuous $\varepsilon$-selection

I. G. Tsar'kov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (501 kB) Citations (21) Russian version article
References:
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DOI: https://doi.org/10.1070/SM8481
Abstract: The paper is concerned with properties of sets admitting a continuous selection from the set of nearly best approximations. Necessary and sufficient conditions are put forward for the existence of continuous additive and multiplicative $\varepsilon$-selections on closed sets. Sufficient conditions are given for the existence of continuous selections for stable set-valued mappings with not-necessarily-convex values.
Bibliography: 8 titles.
Keywords: continuous selection, infinitely connected set, set-valued mapping.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-00022-а
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 13-01-00022-a).
Received: 26.01.2015 and 02.06.2015
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
MSC: Primary 41A65, 54C65; Secondary 28B20, 54C60
Language: English
Original paper language: Russian
Citation: I. G. Tsar'kov, “Continuous $\varepsilon$-selection”, Sb. Math., 207:2 (2016), 267–285
Citation in format AMSBIB
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\paper Continuous $\varepsilon$-selection
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\vol 207
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\pages 267--285
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    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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