电邮这篇文章 Geometry of the Gromov-Hausdorff distance on the class of all metric spaces
- 作者: Borzov S.I.1, Ivanov A.O.2,3,4, Tuzhilin A.A.2
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隶属关系:
- "Pyrus"
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Bauman Moscow State Technical University
- Moscow Center for Fundamental and Applied Mathematics
- 期: 卷 213, 编号 5 (2022)
- 页面: 68-87
- 栏目: Articles
- URL: https://journal-vniispk.ru/0368-8666/article/view/133446
- DOI: https://doi.org/10.4213/sm9651
- ID: 133446
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详细
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.
作者简介
Stanislav Borzov
"Pyrus"
Alexandr 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 Tuzhilin
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Email: tuz@mech.math.msu.su
Doctor of physico-mathematical sciences, Professor
参考
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- M. Gromov, “Groups of polynomial growth and expanding maps”, Inst. Hautes Etudes Sci. Publ. Math., 53 (1981), 53–78
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- A. O. Ivanov, A. A. Tuzhilin, “Isometry group of Gromov–Hausdorff space”, Mat. Vesnik, 71:1-2 (2019), 123–154
- Д. Ю. Бураго, Ю. Д. Бураго, С. В. Иванов, Курс метрической геометрии, Ин-т компьютерных исследований, М.–Ижевск, 2004, 512 с.
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- A. Ivanov, S. Iliadis, A. Tuzhilin, Realizations of Gromov–Hausdorff distance
- S. Chowdhury, F. Memoli, Constructing geodesics on the space of compact metric spaces
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- В. Г. Болтянский, И. Ц. Гохберг, Теоремы и задачи комбинаторной геометрии, Наука, М., 1965, 108 с.
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