Abstract:
Generalized n-piecewise functions constructed from given monotone path-connected boundedly compact subsets of the space C[a,b] are studied. They are shown to be monotone path-connected suns. In finite-dimensional polyhedral spaces, luminosity points of sets admitting a lower semicontinuous selection of the metric projection operator are investigated. An example of a non-B-connected sun in a four-dimensional polyhedral normed space is constructed.
Bibliography: 14 titles.
This work was supported by the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center of Fundamental and Applied Mathematics under agreement no. 075-15-2019-1621.
Citation:
I. G. Tsar'kov, “Solarity and connectedness of sets in the space C[a,b] and in finite-dimensional polyhedral spaces”, Sb. Math., 213:2 (2022), 268–282
\Bibitem{Tsa22}
\by I.~G.~Tsar'kov
\paper Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces
\jour Sb. Math.
\yr 2022
\vol 213
\issue 2
\pages 268--282
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Linking options:
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https://doi.org/10.1070/SM9554
https://www.mathnet.ru/eng/sm/v213/i2/p149
This publication is cited in the following 7 articles:
A. R. Alimov, “Strict protosuns in asymmetric spaces of continuous functions”, Results Math., 78:3 (2023), 95
A. R. Alimov, “On local properties of spaces implying monotone path-connectedness of suns”, J. Anal., 31 (2023), 2287–2295
I. G. Tsar'kov, “Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces”, Izv. Math., 87:4 (2023), 835–851
A. R. Alimov, “Approximative solar properties of sets and local geometry of the unit sphere”, Lobachevskii J. Math., 44:12 (2023), 5148
A. R. Alimov, “Tomograficheskie kharakterizatsionnye teoremy dlya solnts v trekhmernykh prostranstvakh”, Tr. IMM UrO RAN, 28, no. 2, 2022, 45–55
I. G. Tsar'kov, “Approximative and structural properties of sets in asymmetric spaces”, Izv. Math., 86:6 (2022), 1240–1253
A. R. Alimov, I. G. Tsar'kov, “Classical problems of rational approximation”, Dokl. Math., 106:2 (2022), 305–307
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