Email this article Geometry of the Gromov-Hausdorff distance on the class of all metric spaces
- Authors: Borzov S.I.1, Ivanov A.O.2,3,4, Tuzhilin A.A.2
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Affiliations:
- "Pyrus"
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Bauman Moscow State Technical University
- Moscow Center for Fundamental and Applied Mathematics
- Issue: Vol 213, No 5 (2022)
- Pages: 68-87
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/133446
- DOI: https://doi.org/10.4213/sm9651
- ID: 133446
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Abstract
The geometry of the Gromov-Hausdorff distance on the class of all metric spaces considered up to isometry is studied. The concept of a class in the sense of von Neumann-Bernays-Gödel set theory is used. As in the case of compact metric spaces, continuous curves and their lengths are defined, and the Gromov-Hausdorff distance is shown to be intrinsic on the entire class. As an application, metric segments (classes of points lying between two given points) are considered and their extendability beyond endpoints is examined. Bibliography: 13 titles.
About the authors
Stanislav Igorevich Borzov
"Pyrus"
Alexandr Olegovich Ivanov
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Bauman Moscow State Technical University; Moscow Center for Fundamental and Applied Mathematics
Email: aoiva@mech.math.msu.su
Doctor of physico-mathematical sciences, Professor
Alexey Avgustinovich Tuzhilin
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Email: tuz@mech.math.msu.su
Doctor of physico-mathematical sciences, Professor
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