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Sbornik: Mathematics, 2022, Volume 213, Issue 2, Pages 268–282
DOI: https://doi.org/10.1070/SM9554 (Mi sm9554) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces

I. G. Tsar'kov

Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
English version PDF (487 kB) Citations (7)
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DOI: https://doi.org/10.1070/SM9554
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.
Keywords: monotone path-connected set, Menger-connectedness, stably monotone path-connectedness, sun.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1621
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.
Received: 20.01.2021 and 01.03.2021
Russian version:
Matematicheskii Sbornik, 2022, Volume 213, Number 2, Pages 149–166
DOI: https://doi.org/10.4213/sm9554
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
MSC: 41A65
Language: English
Original paper language: Russian
Citation: I. G. Tsar'kov, “Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces”, Mat. Sb., 213:2 (2022), 149–166; Sb. Math., 213:2 (2022), 268–282
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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