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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.
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
Linking options:
https://www.mathnet.ru/eng/mzm507https://doi.org/10.4213/mzm507 https://www.mathnet.ru/eng/mzm/v69/i3/p338
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Abstract page: | 303 | Full-text PDF : | 153 | References: | 42 | First page: | 1 |
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