Geometry and topology

On mappings that preserve metric order

K. G. Kamalutdinov<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
^b Novosibirsk State University, Pirogova Str., 2, 630090, Novosibirsk, Russia

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.

UDC: 515.124

MSC: 54E40, 54B20

Received December 12, 2016, published December 13, 2017

DOI: 10.17377/semi.2017.14.122

Bibliographic databases:

•