This article is cited in 21 scientific papers (total in 21 papers)
Monotone path-connectedness of Chebyshev sets in the space $C(Q)$
A. R. Alimov
M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
The structure of Chebyshev
sets and strict suns in the space $C(Q)$ with compact $Q$ is considered.
It is shown that a boundedly compact strict
sun in $C(Q)$ (in particular, a bounded compact Chebyshev set)
is monotone path-connected and
in particular, $P$-acyclic.
It is demonstrated that a monotone path-connected
Chebyshev set in $C(Q)$ is a sun.
Bibliography: 25 titles.
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Sbornik: Mathematics, 2006, 197:9, 1259–1272
MSC: Primary 41A65; Secondary 46B20
Received: 10.08.2005 and 17.05.2006
A. R. Alimov, “Monotone path-connectedness of Chebyshev sets in the space $C(Q)$”, Mat. Sb., 197:9 (2006), 3–18; Sb. Math., 197:9 (2006), 1259–1272
Citation in format AMSBIB
\paper Monotone path-connectedness of Chebyshev sets in the space~$C(Q)$
\jour Mat. Sb.
\jour Sb. Math.
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A. R. Alimov, “Bounded strict solar property of strict suns in the space $C(Q)$”, Moscow University Mathematics Bulletin, 68:1 (2013), 14–17
A. R. Alimov, “Local solarity of suns in normed linear spaces”, J. Math. Sci., 197:4 (2014), 447–454
A. R. Alimov, “Monotone path-connectedness and solarity of Menger-connected sets in Banach spaces”, Izv. Math., 78:4 (2014), 641–655
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A. R. Alimov, I. G. Tsar'kov, “Connectedness and other geometric properties of suns and Chebyshev sets”, J. Math. Sci., 217:6 (2016), 683–730
A. R. Alimov, “On finite-dimensional Banach spaces in which suns are connected”, Eurasian Math. J., 6:4 (2015), 7–18
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
I. G. Tsar'kov, “Continuous $\varepsilon$-Selection and Monotone Path-Connected Sets”, Math. Notes, 101:6 (2017), 1040–1049
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
Tsar'kov I.G., “Continuous Selection From the Sets of Best and Near-Best Approximation”, Dokl. Math., 96:1 (2017), 362–364
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
Alimov A.R., “On Approximative Properties of Locally Chebyshev Sets”, Proc. Inst. Math. Mech., 44:1 (2018), 36–42
I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. Math., 82:4 (2018), 837–859
I. G. Tsar'kov, “New Criteria for the Existence of a Continuous $\varepsilon$-Selection”, Math. Notes, 104:5 (2018), 727–734
A. R. Alimov, “Selections of the best and near-best approximation operators and solarity”, Proc. Steklov Inst. Math., 303 (2018), 10–17
I. G. Tsar'kov, “Weakly monotone sets and continuous selection from a near-best approximation operator”, Proc. Steklov Inst. Math., 303 (2018), 227–238
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
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