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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 3, Pages 189–216 (Mi izv8450)  

This article is cited in 5 scientific papers (total in 5 papers)

Continuous selection for set-valued mappings

I. G. Tsar'kov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We study properties of set-valued mappings $F$ admitting a continuous selection $f$ which is a continuous $\epsilon$-selection (from the set of $\epsilon$-closest points) for the images $F(x)$ $(x\in X)$. This is interpreted as an $\epsilon$-selection for continuously varying sets in a space with continuously varying norms. We deduce new fixed-point theorems from the results obtained. We also study geometric-topological properties of sets all of whose $r$-neighbourhoods possess a continuous $\epsilon$-selection for every $\epsilon>0$. We obtain a characterization of such sets.

Keywords: $\epsilon$-selection, continuous selection for set-valued mappings, $\overset{ _\circ}{B}$-infinite connectedness, $\overset{ _\circ}{B}$-approximative infinite connectedness, $\overset{ _\circ}{B}$-neighbourhood infinite connectedness, fixed-point theorems.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00022-a
This paper was written with the financial support of the Russian Foundation for Basic Research (grant no. 13-01-00022-a).


DOI: https://doi.org/10.4213/im8450

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English version:
Izvestiya: Mathematics, 2017, 81:3, 645–669

Bibliographic databases:

UDC: 517.982.256
MSC: 54C60, 54C65, 54H25
Received: 21.02.2016
Revised: 11.04.2016

Citation: I. G. Tsar'kov, “Continuous selection for set-valued mappings”, Izv. RAN. Ser. Mat., 81:3 (2017), 189–216; Izv. Math., 81:3 (2017), 645–669

Citation in format AMSBIB
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  • https://doi.org/10.4213/im8450
  • http://mi.mathnet.ru/eng/izv/v81/i3/p189

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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. I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. Math., 82:4 (2018), 837–859  mathnet  crossref  crossref  adsnasa  isi  elib
    2. I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579  mathnet  crossref  crossref  adsnasa  isi  elib
    3. I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Math. Notes, 104:5 (2018), 727–734  mathnet  crossref  crossref  isi  elib
    4. I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238  mathnet  crossref  crossref  isi  elib
    5. I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347  mathnet  crossref  crossref  adsnasa  isi
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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