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Mat. Zametki, 2021, Volume 109, Issue 5, Pages 781–792 (Mi mz12890)  

Properties of Monotone Connected Sets

I. G. Tsar'kov

Moscow Center for Fundamental and Applied Mathematics

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.


DOI: https://doi.org/10.4213/mzm12890

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English version:
Mathematical Notes, 2021, 109:5, 819–827

Bibliographic databases:

UDC: 517.982.256
Received: 08.09.2020

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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