Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2018, Number 6, Pages 3–8 (Mi vmumm578)  
This article is cited in 1 scientific paper (total in 1 paper)

Mathematics

Hausdorff mapping: 1-Lipschitz and isometry properties

I. A. Mikhailov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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Abstract: 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.
Key words: Hausdorff distance, Gromov–Hausdorff space, Hausdorff mapping.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ–6399.2018.1
Received: 22.12.2017
English version:
Moscow University Mathematics Bulletin, 2018, Volume 73, Issue 6, Pages 211–216
DOI: https://doi.org/10.3103/S0027132218060013
Bibliographic databases:
Document Type: Article
UDC: 514
Language: Russian
Citation: I. A. Mikhailov, “Hausdorff mapping: 1-Lipschitz and isometry properties”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2018, no. 6, 3–8; Moscow University Mathematics Bulletin, 73:6 (2018), 211–216
Citation in format AMSBIB
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