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Russian Mathematical Surveys, 2002, Volume 57, Issue 2, Pages 221–240
DOI: https://doi.org/10.1070/RM2002v057n02ABEH000495 (Mi rm495) 		 
This article is cited in 21 scientific papers (total in 21 papers)

Metrically homogeneous spaces

S. A. Bogatyi

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (273 kB) Citations (21)
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DOI: https://doi.org/10.1070/RM2002v057n02ABEH000495
Abstract: This survey discusses the problem of describing properties of the class of metric spaces in which the Uryson construction of a universal homogeneous metric space (for this class) can be carried out axiomatically. One of the main properties of this kind is the possibility of gluing together two metrics given on closed subsets and coinciding on their intersection. The uniqueness problem for a (countable or complete) homogeneous space universal in a given class of metric spaces is discussed. The problem of extending a Clifford translation of a compact subset of an (ultrametric) Uryson space to a Clifford translation of the entire Uryson space is studied.
Received: 08.10.2001
Russian version:
Uspekhi Matematicheskikh Nauk, 2002, Volume 57, Issue 2(344), Pages 3–22
DOI: https://doi.org/10.4213/rm495
Bibliographic databases:
Document Type: Article
UDC: 515.124.4
MSC: Primary 54E35, 54C25, 54C20; Secondary 22F30, 54E45, 54E25, 54E40
Language: English
Original paper language: Russian
Citation: S. A. Bogatyi, “Metrically homogeneous spaces”, Uspekhi Mat. Nauk, 57:2(344) (2002), 3–22; Russian Math. Surveys, 57:2 (2002), 221–240
Citation in format AMSBIB
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    • This publication is cited in the following 21 articles:
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