I. G. Tsar'kov, “Properties of monotone path-connected sets”, Izv. Math., 85:2 (2021), 306

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Izvestiya: Mathematics, 2021, Volume 85, Issue 2, Pages 306–331
DOI: https://doi.org/10.1070/IM8995 (Mi im8995)

This article is cited in 16 scientific papers (total in 16 papers)

Properties of monotone path-connected sets

I. G. Tsar'kov^ab

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

English version PDF (550 kB) Citations (16) Russian version article

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DOI: https://doi.org/10.1070/IM8995

Abstract: We study monotone path-connected sets and also strongly and weakly Menger-connected sets. We introduce the notion of

ε

$\varepsilon$ -solarity and establish a connection with the notion of solarity. We prove that boundedly compact suns in

C (Q)

$C(Q)$ 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).

Received: 27.11.2019
Revised: 24.07.2020

Bibliographic databases:

Document Type: Article

UDC: 517.982.256

MSC: 41A65, 52A30, 54C65

Language: English

Original paper language: Russian

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

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/im8995

https://doi.org/10.1070/IM8995

https://www.mathnet.ru/eng/im/v85/i2/p142

This publication is cited in the following 16 articles:

I. G. Tsarkov, “Svoistva diskretnogo ne bolee chem schetnogo ob'edineniya mnozhestv v nesimmetrichnykh prostranstvakh”, Matem. sb., 216:2 (2025), 128–144
P. A. Borodin, E. A. Savinova, “Any Chebyshev curve without self-intersections is monotone”, Math. Notes, 116:2 (2024), 387–389
E. A. Savinova, “Sets in $\mathbb {R}^n$ monotone path-connected with respect to some norm”, Moscow University Mathematics Bulletin, 78:1 (2023), 49–51
I. G. Tsar'kov, “Connectedness in asymmetric spaces”, J. Math. Anal. Appl., 527:1 (2023), 127381
A. R. Alimov, “On local properties of spaces implying monotone path-connectedness of suns”, J. Anal., 31 (2023), 2287–2295
I. G. Tsar'kov, “Continuous selections of set-valued mappings and approximation in asymmetric and semilinear spaces”, Izv. Math., 87:4 (2023), 835–851
B. B. Bednov, “Three-Dimensional Spaces Where All Bounded Chebyshev Sets Are Monotone Path Connected”, Math. Notes, 114:3 (2023), 283–295
I. G. Tsar'kov, “Solarity and connectedness of sets in the space $C[a,b]$ and in finite-dimensional polyhedral spaces”, Sb. Math., 213:2 (2022), 268–282
A. R. Alimov, “Tomograficheskie kharakterizatsionnye teoremy dlya solnts v trekhmernykh prostranstvakh”, Tr. IMM UrO RAN, 28, no. 2, 2022, 45–55
I. G. Tsar'kov, “Uniformly and locally convex asymmetric spaces”, Sb. Math., 213:10 (2022), 1444–1469
I. G. Tsar'kov, “Approximative and structural properties of sets in asymmetric spaces”, Izv. Math., 86:6 (2022), 1240–1253
I. G. Tsar'kov, “Density of the Points of Continuity of the Metric Function and Projection in Asymmetric Spaces”, Math. Notes, 112:6 (2022), 1017–1024
I. G. Tsarkov, “Uniformly and locally convex asymmetric spaces”, Russ. J. Math. Phys., 29:1 (2022), 141–148
A. R. Alimov, I. G. Tsarkov, “Solarity and proximinality in generalized rational approximation in spaces $C(Q)$ and $L^p$ ”, Russ. J. Math. Phys., 29:3 (2022), 291–305
A. R. Alimov, “Monotone path-connectedness of strict suns”, Lobachevskii J. Math., 43:3 (2022), 519–527
I. G. Tsar'kov, “Properties of suns in the spaces $L^1$ and $C(Q)$ ”, Russ. J. Math. Phys., 28:3 (2021), 398–405

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Известия Российской академии наук. Серия математическая

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Abstract page:	514
Russian version PDF:	131
English version PDF:	83
Russian version HTML:	155
References:	64
First page:	9

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