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Matematicheskie Zametki, 2021, Volume 109, Issue 5, Pages 781–792
DOI: https://doi.org/10.4213/mzm12890 (Mi mzm12890) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Properties of Monotone Connected Sets

I. G. Tsar'kov

Moscow Center for Fundamental and Applied Mathematics
Full-text PDF (508 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm12890
Abstract: Properties of Menger-monotone sets are studied. It is proved that all boundedly weakly compact Menger-connected $(\omega\rhd n)$-approximatively compact sets are suns. The existence of a continuous selection of the Chebyshev near-center map (relative to $V$) is proved for the case in which $V\subset C(Q)$ is a $B^2$-infinitely connected set in the space $C(Q)$.
Keywords: Menger-monotone set, Menger-connected set, sun.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00332
This work was supported by the Russian Foundation for Basic Research under grant 19-01-00332-a.
Received: 08.09.2020
English version:
Mathematical Notes, 2021, Volume 109, Issue 5, Pages 819–827
DOI: https://doi.org/10.1134/S0001434621050138
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
Language: Russian
Citation: I. G. Tsar'kov, “Properties of Monotone Connected Sets”, Mat. Zametki, 109:5 (2021), 781–792; Math. Notes, 109:5 (2021), 819–827
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v109/i5/p781
    • This publication is cited in the following 4 articles:
    1. A. R. Alimov, I. G. Tsar'kov, “Monotone path-connected sets in geometric approximation theory and their applications”, jour, 2:2 (2024), 30  crossref
    2. A. R. Alimov, “On local properties of spaces implying monotone path-connectedness of suns”, J. Anal., 31:3 (2023), 2287  crossref  mathscinet
    3. A. R. Alimov, “Tomograficheskie kharakterizatsionnye teoremy dlya solnts v trekhmernykh prostranstvakh”, Tr. IMM UrO RAN, 28, no. 2, 2022, 45–55  mathnet  crossref  elib
    4. A. R. Alimov, I. G. Tsar'kov, “Solarity and proximinality in generalized rational approximation in spaces $C(Q)$ and $L^p$”, Russ. J. Math. Phys., 29:3 (2022), 291  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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