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 Uspekhi Mat. Nauk, 2002, Volume 57, Issue 2(344), Pages 3–22 (Mi umn495)

Metrically homogeneous spaces

S. A. Bogatyi

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

DOI: https://doi.org/10.4213/rm495

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English version:
Russian Mathematical Surveys, 2002, 57:2, 221–240

Bibliographic databases:

UDC: 515.124.4
MSC: Primary 54E35, 54C25, 54C20; Secondary 22F30, 54E45, 54E25, 54E40

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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