Varieties of topological groups, Lie groups and SIN-groups

Karl Hofmann; Sidney Morris; Markus Stroppel

Colloquium Mathematicae (1996)

  • Volume: 70, Issue: 2, page 151-163
  • ISSN: 0010-1354

Abstract

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In this paper we answer three open problems on varieties of topological groups by invoking Lie group theory. We also reprove in the present context that locally compact groups with arbitrarily small invariant identity neighborhoods can be approximated by Lie groups

How to cite

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Hofmann, Karl, Morris, Sidney, and Stroppel, Markus. "Varieties of topological groups, Lie groups and SIN-groups." Colloquium Mathematicae 70.2 (1996): 151-163. <http://eudml.org/doc/210402>.

@article{Hofmann1996,
abstract = {In this paper we answer three open problems on varieties of topological groups by invoking Lie group theory. We also reprove in the present context that locally compact groups with arbitrarily small invariant identity neighborhoods can be approximated by Lie groups},
author = {Hofmann, Karl, Morris, Sidney, Stroppel, Markus},
journal = {Colloquium Mathematicae},
keywords = {pro-Lie group; varieties of topological groups; IN-group; SIN-group; Lie group; abelian topological group; Heisenberg group; Lie groups; SIN groups},
language = {eng},
number = {2},
pages = {151-163},
title = {Varieties of topological groups, Lie groups and SIN-groups},
url = {http://eudml.org/doc/210402},
volume = {70},
year = {1996},
}

TY - JOUR
AU - Hofmann, Karl
AU - Morris, Sidney
AU - Stroppel, Markus
TI - Varieties of topological groups, Lie groups and SIN-groups
JO - Colloquium Mathematicae
PY - 1996
VL - 70
IS - 2
SP - 151
EP - 163
AB - In this paper we answer three open problems on varieties of topological groups by invoking Lie group theory. We also reprove in the present context that locally compact groups with arbitrarily small invariant identity neighborhoods can be approximated by Lie groups
LA - eng
KW - pro-Lie group; varieties of topological groups; IN-group; SIN-group; Lie group; abelian topological group; Heisenberg group; Lie groups; SIN groups
UR - http://eudml.org/doc/210402
ER -

References

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  1. [1] R. W. Bagley, T. S. Wu and J. S. Yang, Pro-Lie groups, Trans. Amer. Math. Soc. 287 (1985), 829-838. Zbl0575.22006
  2. [2] N. Bourbaki, Topologie générale, Chap. 1, Hermann, Paris, 1965. 
  3. [3] M. S. Brooks, S. A. Morris and S. A. Saxon, Generating varieties of topological groups, Proc. Edinburgh Math. Soc. 18 (1973), 191-197. Zbl0263.22002
  4. [4] V. M. Gluškov [V. M. Glushkov], The structure of locally compact groups and Hilbert's Fifth Problem, Uspekhi Mat. Nauk 12 (2) (1957), 3-41 (in Russian); English transl.: Amer. Math. Soc. Transl. Ser. 2 15 (1960), 55-93. 
  5. [5] S. Grosser and M. Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1-40. Zbl0219.22011
  6. [6] K. H. Hofmann and P. S. Mostert, Splitting in topological groups, Mem. Amer. Math. Soc. 43 (1963). Zbl0163.02705
  7. [7] K. Iwasawa, Topological groups with invariant neighborhoods of the identity, Ann. of Math. 54 (1951), 345-348. Zbl0044.01903
  8. [8] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, New York, 1955. Zbl0068.01904
  9. [9] S. A. Morris, Lie groups in varieties of topological groups, Colloq. Math. 30 (1974), 229-235. Zbl0301.22004
  10. [10] S. A. Morris, Varieties of topological groups: A survey, ibid. 46 (1982), 147-165. Zbl0501.22002
  11. [11] S. A. Morris and N. Kelly, Varieties of topological groups generated by groups with invariant compact neighborhoods of the identity, Mat. Časopis Sloven. Akad. Vied 25 (1975), 207-210. Zbl0311.22004

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