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Fundam. Prikl. Mat., 2014, Volume 19, Issue 4, Pages 21–91 (Mi fpm1597)  

This article is cited in 18 scientific papers (total in 18 papers)

Connectedness and other geometric properties of suns and Chebyshev sets

A. R. Alimov, I. G. Tsar'kov

Lomonosov Moscow State University

Abstract: This survey is concerned with structural characteristics of “suns” in normed linear spaces. Special attention is paid to connectedness and monotone path-connectedness of suns. We address both direct theorems of the geometric approximation theory, in which approximative properties of sets are derived from their structural characteristics, and inverse theorems, in which from approximative characteristics of sets one derives their structural properties.

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English version:
Journal of Mathematical Sciences (New York), 2016, 217:6, 683–730

Bibliographic databases:

UDC: 517.982.256

Citation: A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, Fundam. Prikl. Mat., 19:4 (2014), 21–91; J. Math. Sci., 217:6 (2016), 683–730

Citation in format AMSBIB
\by A.~R.~Alimov, I.~G.~Tsar'kov
\paper Connectedness and other geometric properties of suns and Chebyshev sets
\jour Fundam. Prikl. Mat.
\yr 2014
\vol 19
\issue 4
\pages 21--91
\jour J. Math. Sci.
\yr 2016
\vol 217
\issue 6
\pages 683--730

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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. A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18  mathnet
    2. I. G. Tsar'kov, “Continuous $\varepsilon$-selection”, Sb. Math., 207:2 (2016), 267–285  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. R. Alimov, I. G. Tsar'kov, “Connectedness and solarity in problems of best and near-best approximation”, Russian Math. Surveys, 71:1 (2016), 1–77  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. I. G. Tsar'kov, “Local and global continuous $\varepsilon$-selection”, Izv. Math., 80:2 (2016), 442–461  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. A. R. Alimov, “Prostranstva Mazura i 4.3-svoistvo peresecheniya $(BM)$-prostranstv”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:2 (2016), 133–137  mathnet  crossref  mathscinet  elib
    6. I. G. Tsar'kov, “Continuous selection for set-valued mappings”, Izv. Math., 81:3 (2017), 645–669  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. 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
    8. A. R. Alimov, “Selections of the metric projection operator and strict solarity of sets with continuous metric projection”, Sb. Math., 208:7 (2017), 915–928  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. A. R. Alimov, “A monotone path-connected set with outer radially lower continuous metric projection is a strict sun”, Siberian Math. J., 58:1 (2017), 11–15  mathnet  crossref  crossref  isi  elib  elib
    10. I. G. Tsar'kov, “Continuous selection from the sets of best and near-best approximation”, Dokl. Math., 96:1 (2017), 362–364  crossref  mathscinet  zmath  isi  elib  scopus
    11. 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
    12. I. G. Tsar'kov, “Continuous selections in asymmetric spaces”, Sb. Math., 209:4 (2018), 560–579  mathnet  crossref  crossref  adsnasa  isi  elib
    13. 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
    14. A. R. Alimov, “Ogranichennaya styagivaemost strogikh solnts v trëkhmernykh prostranstvakh”, Fundament. i prikl. matem., 22:1 (2018), 3–11  mathnet  mathscinet
    15. 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
    16. 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
    17. I. G. Tsar'kov, “Smooth solutions of the eikonal equation and the behaviour of local minima of the distance function”, Izv. Math., 83:6 (2019), 1234–1258  mathnet  crossref  crossref  adsnasa  isi
    18. 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
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