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Izv. RAN. Ser. Mat., 2016, Volume 80, Issue 2, Pages 165–184 (Mi izv8348)  

This article is cited in 10 scientific papers (total in 10 papers)

Local and global continuous $\varepsilon$-selection

I. G. Tsar'kov

M. V. Lomonosov Moscow State University

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).


DOI: https://doi.org/10.4213/im8348

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English version:
Izvestiya: Mathematics, 2016, 80:2, 442–461

Bibliographic databases:

UDC: 517.982.256
MSC: 46B20, 54C65, 41A65
Received: 01.02.2015
Revised: 03.06.2015

Citation: I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. RAN. Ser. Mat., 80:2 (2016), 165–184; Izv. Math., 80:2 (2016), 442–461

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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 selection for set-valued mappings”, Izv. Math., 81:3 (2017), 645–669  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. I. G. Tsar'kov, “Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets”, Math. Notes, 101:6 (2017), 1040–1049  mathnet  crossref  crossref  mathscinet  isi  elib
    3. I. G. Tsar'kov, “Continuous selection from the sets of best and near-best approximation”, Dokl. Math., 96:1 (2017), 362–364  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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
    5. I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579  mathnet  crossref  crossref  adsnasa  isi  elib
    6. 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
    7. A. R. Alimov, “Ogranichennaya styagivaemost strogikh solnts v trëkhmernykh prostranstvakh”, Fundament. i prikl. matem., 22:1 (2018), 3–11  mathnet
    8. A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17  mathnet  crossref  crossref  isi  elib
    9. 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
    10. Alimov A.R., “Continuity of the Metric Projection and Local Solar Properties of Sets: Continuity of the Metric Projection and Solar Properties”, Set-Valued Var. Anal., 27:1 (2019), 213–222  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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