Varieties of topological groups, Lie groups and SIN-groups

• Autorzy: Karl H. Hofmann , Sidney A. Morris , Markus Stroppel
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

pro-Lie group; varieties of topological groups; IN-group; SIN-group; Lie group

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1996
• Tom: 70
• Numer: 2
• Strony: 151-163

Daty

wydano

1996

otrzymano

1994-08-04

poprawiono

1995-02-28

Twórcy

autor

Karl H. Hofmann

• Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstr. 7, D-64289 Darmstadt, Germany

autor

Sidney A. Morris

• Faculty of Informatics, University of Wollongong, Wollongong, NSW 2522, Australia

autor

Markus Stroppel

• Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstr. 7, D-64289 Darmstadt, Germany

Bibliografia

• [1] R. W. Bagley, T. S. Wu and J. S. Yang, Pro-Lie groups, Trans. Amer. Math. Soc. 287 (1985), 829-838.
• [2] N. Bourbaki, Topologie générale, Chap. 1, Hermann, Paris, 1965.
• [3] M. S. Brooks, S. A. Morris and S. A. Saxon, Generating varieties of topological groups, Proc. Edinburgh Math. Soc. 18 (1973), 191-197.
• [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] S. Grosser and M. Moskowitz, Compactness conditions in topological groups, J. Reine Angew. Math. 246 (1971), 1-40.
• [6] K. H. Hofmann and P. S. Mostert, Splitting in topological groups, Mem. Amer. Math. Soc. 43 (1963).
• [7] K. Iwasawa, Topological groups with invariant neighborhoods of the identity, Ann. of Math. 54 (1951), 345-348.
• [8] D. Montgomery and L. Zippin, Topological Transformation Groups, Interscience, New York, 1955.
• [9] S. A. Morris, Lie groups in varieties of topological groups, Colloq. Math. 30 (1974), 229-235.
• [10] S. A. Morris, Varieties of topological groups: A survey, ibid. 46 (1982), 147-165.
• [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.