Geodesic
Hausdorff mapping: 1-Lipschitz and isometry properties
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2018), pp. 3-8

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

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},
     publisher = {mathdoc},
     number = {6},
     year = {2018},
     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
PB  - mathdoc
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
%I mathdoc
%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/