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Mat. Zametki, 2001, Volume 69, Issue 3, Pages 338–345 (Mi mz507)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Properties of Plesio-Uniform Subgroups in Lie Groups

V. V. Gorbatsevich

Moscow State Technological University "Stankin"

Abstract: The paper is devoted to the study of properties of a class of subgroups $H$ in Lie groups $G$ that was recently introduced by the author. A closed subgroup $H$ in a Lie group $G$ is said to be plesio-uniform if there is a closed subgroup $P$ of $G$ that contains $H$ and for which $P$ is uniform in $G$ and $H$ is quasi-uniform in $P$. In the paper we give answers to several natural questions concerning plesio-uniform subgroups. It is proved that one obtains the same notion of plesio-uniformity when transposing the conditions of uniformity and quasi-uniformity in the definition of plesio-uniformity of a subgroup. If a closed subgroup $H$ of $G$ contains a plesio-uniform subgroup, then $H$ is also plesio-uniform. Other properties of plesio-uniform subgroups are also considered.

DOI: https://doi.org/10.4213/mzm507

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English version:
Mathematical Notes, 2001, 69:3, 306–312

Bibliographic databases:

UDC: 519.4
Received: 02.11.1999
Revised: 19.05.2000

Citation: V. V. Gorbatsevich, “On the Properties of Plesio-Uniform Subgroups in Lie Groups”, Mat. Zametki, 69:3 (2001), 338–345; Math. Notes, 69:3 (2001), 306–312

Citation in format AMSBIB
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\jour Mat. Zametki
\yr 2001
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\pages 338--345
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\zmath{https://zbmath.org/?q=an:0989.22014}
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\transl
\jour Math. Notes
\yr 2001
\vol 69
\issue 3
\pages 306--312
\crossref{https://doi.org/10.1023/A:1010223222690}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. V. Gorbatsevich, “Compact Homogeneous Spaces and Their Generalizations”, Journal of Mathematical Sciences, 153:6 (2008), 763–798  mathnet  crossref  mathscinet  zmath  elib
    2. V. V. Gorbatsevich, “On quasicompact homogeneous spaces”, Siberian Math. J., 54:2 (2013), 231–242  mathnet  crossref  mathscinet  isi
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