Action of Similarity Transformations on Families of Metric Spaces
- Authors: Bogatyi S.A.1, Tuzhilin A.A.1
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Affiliations:
- Московский государственный университет им. М. В. Ломоносова
- Issue: Vol 223 (2023)
- Pages: 3-13
- Section: Articles
- URL: https://ogarev-online.ru/2782-4438/article/view/270823
- DOI: https://doi.org/10.36535/0233-6723-2023-223-3-13
- ID: 270823
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Abstract
We study the action of the multiplicative group of positive real numbers on various families of a metric space, which consists of multiplying all distances in the metric space by the same positive real number; such an action is called similarity. Stationary subgroups of such actions are studied.
About the authors
S. A. Bogatyi
Московский государственный университет им. М. В. Ломоносова
Author for correspondence.
Email: bogatyi@inbox.ru
Russian Federation, Москва
A. A. Tuzhilin
Московский государственный университет им. М. В. Ломоносова
Email: tuz@mech.math.msu.su
Russian Federation, Москва
References
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- Мендельсон Э. Введение в математическую логику. — М.: Наука, 1984.
- Edwards D. The structure of superspace// in: Studies in Topology (Stavrakas N. M., Allen K. R., ed.). — New York–London–San Francisco: Academic Press, 1975. — P. 121–133.
- Gromov M. Structures métriques pour les variétés riemanniennes. — CEDIC/Fernand Nathan, 1981.
- Gromov M. Metric structures for Riemannian and non-Riemannian spaces. — Birkhäuser, 1999.
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