Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2019, Number 2, Pages 42–46 (Mi vmumm613)  
This article is cited in 2 scientific papers (total in 2 papers)

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Path connectedness of spheres in Gromov–Hausdorff space

R. A. Tsvetnikov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (179 kB) Citations (2)
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Abstract: The path connectedness of spheres in Gromov–Hausdorff space is studied. The following two assertions are proved: (1) each sphere centered at one-point space is path connected; (2) for any metric space $X$ there exists a number $R_X$ such that each sphere with the center at $X$ and radius greater than $R_X$ is path connected.
Key words: Gromov–Hausdorff metric, path connectedness.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-6399.2018.1
Russian Foundation for Basic Research 16-01-00378-а
Received: 27.04.2018
English version:
Moscow University Mathematics Bulletin, 2019, Volume 74, Issue 2, Pages 70–74
DOI: https://doi.org/10.3103/S0027132219020062
Bibliographic databases:
Document Type: Article
UDC: 515.124
Language: Russian
Citation: R. A. Tsvetnikov, “Path connectedness of spheres in Gromov–Hausdorff space”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2019, no. 2, 42–46; Moscow University Mathematics Bulletin, 74:2 (2019), 70–74
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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