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

This article is cited in 14 scientific papers (total in 14 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

Citation in format AMSBIB
\by I.~G.~Tsar'kov
\paper Local and global continuous $\varepsilon$-selection
\jour Izv. RAN. Ser. Mat.
\yr 2016
\vol 80
\issue 2
\pages 165--184
\jour Izv. Math.
\yr 2016
\vol 80
\issue 2
\pages 442--461

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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathscinet  adsnasa  isi  elib
    5. I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579  mathnet  crossref  crossref  mathscinet  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  mathscinet  isi  elib
    7. A. R. Alimov, “Ogranichennaya styagivaemost strogikh solnts v trëkhmernykh prostranstvakh”, Fundament. i prikl. matem., 22:1 (2018), 3–11  mathnet  mathscinet
    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  mathscinet  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  mathscinet  isi  elib
    10. A. R. Alimov, “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
    11. I. G. Tsar'kov, “Local Approximation Properties of Sets and Continuous Selections on Them”, Math. Notes, 106:6 (2019), 995–1008  mathnet  crossref  crossref  mathscinet  isi  elib
    12. I. G. Tsar'kov, “Weakly monotone sets and continuous selection in asymmetric spaces”, Sb. Math., 210:9 (2019), 1326–1347  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    13. I. G. Tsar'kov, “Approximative properties of sets and continuous selections”, Sb. Math., 211:8 (2020), 1190–1211  mathnet  crossref  crossref  isi  elib
    14. I. G. Tsar'kov, “Properties of monotone path-connected sets”, Izv. Math., 85:2 (2021), 306–331  mathnet  crossref  crossref  isi  elib
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