Geodesic
Hausdorff mapping: 1-Lipschitz and isometry properties
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2018), pp. 3-8 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The properties of the Hausdorff mapping $\mathcal{H}$ taking each compact metric space to the space of its nonempty closed subspaces endowed with the Hausdorff metric are studied. It is shown that this mapping is nonexpanding (Lipschitz mapping with the constant $1$). Several examples of classes of metric spaces the distances between which are preserved by the mapping $\mathcal{H}$ are presented. The distance between any connected metric space with a finite diameter and any simplex with the greater diameter is calculated. Some properties of the Hausdorff mapping are discussed, which may help to understand whether the mapping $\mathcal{H}$ is isometric or not. 
@article{VMUMM_2018_6_a0,
     author = {I. A. Mikhailov},
     title = {Hausdorff mapping: {1-Lipschitz} and isometry properties},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--8},
     year = {2018},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_6_a0/}
}
TY  - JOUR
AU  - I. A. Mikhailov
TI  - Hausdorff mapping: 1-Lipschitz and isometry properties
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2018
SP  - 3
EP  - 8
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2018_6_a0/
LA  - ru
ID  - VMUMM_2018_6_a0
ER  - 
%0 Journal Article
%A I. A. Mikhailov
%T Hausdorff mapping: 1-Lipschitz and isometry properties
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2018
%P 3-8
%N 6
%U http://geodesic.mathdoc.fr/item/VMUMM_2018_6_a0/
%G ru
%F VMUMM_2018_6_a0
I. A. Mikhailov. Hausdorff mapping: 1-Lipschitz and isometry properties. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2018), pp. 3-8. http://geodesic.mathdoc.fr/item/VMUMM_2018_6_a0/

[1] Ivanov A., Tuzhilin A., Local structure of Gromov–Hausdorff space near finite metric spaces in general position, 2016, arXiv: 1611.04484 [math.MG] | MR

[2] Burago D.Yu., Burago Yu. D., Ivanov S. V., Kurs metricheskoi geometrii, Institut kompyuternykh issledovanii, M.–Izhevsk, 2004 | MR

[3] Ivanov A., Tuzhilin A., Geometry of compact metric space in terms of Gromov–Hausdorff distances to regular simplexes, 2016, arXiv: 1607.06655 [math.MG] | MR

[4] Borsuk K., Mazurkiewicz S., “Sur l'hyperespace d'un continu”, Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie, 24 (1931), 149–152 | MR