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Izv. RAN. Ser. Mat., 2021, Volume 85, Issue 2, Pages 142–171 (Mi izv8995)  

Properties of monotone path-connected sets

I. G. Tsar'kovab

a Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Moscow Center for Fundamental and Applied Mathematics

Abstract: We study monotone path-connected sets and also strongly and weakly Menger-connected sets. We introduce the notion of $\varepsilon$-solarity and establish a connection with the notion of solarity. We prove that boundedly compact suns in $C(Q)$ are monotone path-connected.

Keywords: spans, monotone path-connected sets, Menger connectedness, solarity.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00332-a
This paper was written with the financial support of the Russian Foundation of Basic Research (grant no. 19-01-00332-a).


DOI: https://doi.org/10.4213/im8995

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English version:
Izvestiya: Mathematics, 2021, 85:2, 306–331

Bibliographic databases:

UDC: 517.982.256
MSC: 41A65, 52A30, 54C65
Received: 27.11.2019
Revised: 24.07.2020

Citation: I. G. Tsar'kov, “Properties of monotone path-connected sets”, Izv. RAN. Ser. Mat., 85:2 (2021), 142–171; Izv. Math., 85:2 (2021), 306–331

Citation in format AMSBIB
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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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