Geodesic
On mappings that preserve metric order
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1434-1439.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SEMR_2017_14_a67,
     author = {K. G. Kamalutdinov},
     title = {On mappings that preserve metric order},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1434--1439},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a67/}
}
TY  - JOUR
AU  - K. G. Kamalutdinov
TI  - On mappings that preserve metric order
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2017
SP  - 1434
EP  - 1439
VL  - 14
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2017_14_a67/
LA  - ru
ID  - SEMR_2017_14_a67
ER  - 
%0 Journal Article
%A K. G. Kamalutdinov
%T On mappings that preserve metric order
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2017
%P 1434-1439
%V 14
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2017_14_a67/
%G ru
%F SEMR_2017_14_a67
K. G. Kamalutdinov. On mappings that preserve metric order. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1434-1439. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a67/

[1] P.M. Gruber, G. Lettl, “Isometries of the space of compact subsets of $E^{d}$”, Stud. Sci. Math. Hung., 14 (1979), 169–181 | MR | Zbl

[2] Ch. Bandt, “On the metric structure of hyperspaces with Hausdorff metric”, Math. Nachr., 129 (1986), 175–183 | DOI | MR | Zbl

[3] V.V. Aseev, A.V. Tetenov, A.P. Maksimova, “The Generalized Pompeiu Metric in the Isometry Problem for Hyperspaces”, Math. Notes, 78:1–2 (2005), 149–155 | DOI | MR | Zbl

[4] K. Kuratowski, Topology, v. 2, Academic Press, New York, 1968 | MR