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Sibirskii Matematicheskii Zhurnal, 2022, Volume 63, Number 5, Pages 975–993
DOI: https://doi.org/10.33048/smzh.2022.63.502 (Mi smj7707) 		 
Bounded turning in Möbius structures

V. V. Aseev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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DOI: https://doi.org/10.33048/smzh.2022.63.502
Abstract: We study a Möbius-invariant generalization, called BTR, of the classical property of bounded turning in a metric space which was introduced by Tukia and Väisälä in 1980 and suitable for use in Ptolemaic Möbius structures in the sense of Buyalo. In particular, we prove that every continuum with the BTR property, lying on the boundary of a domain in the complex plane, is locally connected.
Keywords: Möbius structure, Ptolemaic Möbius space, continuum with bounded turning, quasimöbius arc, quasimöbiusly connected space, local connectedness.
Funding agency Grant number
Siberian Branch of Russian Academy of Sciences 1.1.2, проект № 0314-2019-0007
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314–2019–0007).
Received: 23.11.2021
Revised: 25.05.2022
Accepted: 15.06.2022
English version:
Siberian Mathematical Journal, 2022, Volume 63, Issue 5, Pages 819–833
DOI: https://doi.org/10.1134/S0037446622050020
Document Type: Article
UDC: 517.54
MSC: 35R30
Language: Russian
Citation: V. V. Aseev, “Bounded turning in Möbius structures”, Sibirsk. Mat. Zh., 63:5 (2022), 975–993; Siberian Math. J., 63:5 (2022), 819–833
Citation in format AMSBIB
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\by V.~V.~Aseev
\paper Bounded turning in M\"obius structures
\jour Sibirsk. Mat. Zh.
\yr 2022
\vol 63
\issue 5
\pages 975--993
\mathnet{http://mi.mathnet.ru/smj7707}
\crossref{https://doi.org/10.33048/smzh.2022.63.502}
\transl
\jour Siberian Math. J.
\yr 2022
\vol 63
\issue 5
\pages 819--833
\crossref{https://doi.org/10.1134/S0037446622050020}
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    		Сибирский математический журнал Siberian Mathematical Journal
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