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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2017, Volume 14, Pages 1434–1439
DOI: https://doi.org/10.17377/semi.2017.14.122 (Mi semr881) 		 
Geometry and topology

On mappings that preserve metric order

K. G. Kamalutdinovab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova Str., 2, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.17377/semi.2017.14.122
Abstract: We define mappings that preserve metric order and show that they determine the classification of metric spaces. It is proved that the cardinality of set of nontrivial isometries of hyperspace with Hausdorff metric over the metric space $X$ depends only on the metric order of $X$. We also deduce some properties of mappings that preserve metric order of continua.
Keywords: metric, nontrivial isometry, hyperspace, continuum.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00414_а
16-31-00138_мол_а
Received December 12, 2016, published December 13, 2017
Bibliographic databases:
Document Type: Article
UDC: 515.124
MSC: 54E40, 54B20
Language: Russian
Citation: K. G. Kamalutdinov, “On mappings that preserve metric order”, Sib. Èlektron. Mat. Izv., 14 (2017), 1434–1439
Citation in format AMSBIB
\Bibitem{Kam17}
\by K.~G.~Kamalutdinov
\paper On mappings that preserve metric order
\jour Sib. \`Elektron. Mat. Izv.
\yr 2017
\vol 14
\pages 1434--1439
\mathnet{http://mi.mathnet.ru/semr881}
\crossref{https://doi.org/10.17377/semi.2017.14.122}
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