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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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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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