Compactness properties of topological groups. III

Wang, S. P.

doi:10.1090/S0002-9947-1975-0374329-X

Compactness properties of topological groups. III
HTML articles powered by AMS MathViewer

by S. P. Wang

Trans. Amer. Math. Soc. 209 (1975), 399-418

DOI: https://doi.org/10.1090/S0002-9947-1975-0374329-X

PDF | Request permission

Abstract:

Compactness properties of topological groups and finiteness of Haar measure on homogeneous spaces are studied. Some concrete structure theorems are presented.

References

Reinhold Baer, Finiteness properties of groups, Duke Math. J. 15 (1948), 1021–1032. MR 27760

Theory of Lie groups

7

Morikuni Goto, Dense imbeddings of locally compact connected groups, Ann. of Math. (2) 61 (1955), 154–169. MR 65567, DOI 10.2307/1969626
Morikuni Goto, A remark on a theorem of A. Weil, Proc. Amer. Math. Soc. 20 (1969), 163–165. MR 232888, DOI 10.1090/S0002-9939-1969-0232888-4
Siegfried Grosser and Martin Moskowitz, On central topological groups, Bull. Amer. Math. Soc. 72 (1966), 826–830. MR 194554, DOI 10.1090/S0002-9904-1966-11575-6
Kenkichi Iwasawa, On some types of topological groups, Ann. of Math. (2) 50 (1949), 507–558. MR 29911, DOI 10.2307/1969548
Kenkichi Iwasawa, Topological groups with invariant compact neighborhoods of the identity, Ann. of Math. (2) 54 (1951), 345–348. MR 43106, DOI 10.2307/1969536
G. D. Mostow, Homogeneous spaces with finite invariant measure, Ann. of Math. (2) 75 (1962), 17–37. MR 145007, DOI 10.2307/1970416
B. H. Neumann, Groups with finite classes of conjugate elements, Proc. London Math. Soc. (3) 1 (1951), 178–187. MR 43779, DOI 10.1112/plms/s3-1.1.178

Continuous groups

Topological groups

1

Carl Ludwig Siegel, Discontinuous groups, Ann. of Math. (2) 44 (1943), 674–689. MR 9959, DOI 10.2307/1969104
J. Tits, Automorphismes à déplacement borné des groupes de Lie, Topology 3 (1964), no. suppl, suppl. 1, 97–107 (French). MR 158948, DOI 10.1016/0040-9383(64)90007-2

A certain class of topological groups

144

3

25

V. I. Ušakov, Topological $\overline {FC}$-groups, Sibirsk. Mat. Ž. 4 (1963), 1162–1174 (Russian). MR 0165031
V. I. Ušakov, Classes of conjugate subgroups in topological groups, Dokl. Akad. Nauk SSSR 190 (1970), 51–53 (Russian). MR 0257267
S. P. Wang, Compactness properties of topological groups, Trans. Amer. Math. Soc. 154 (1971), 301–314. MR 271269, DOI 10.1090/S0002-9947-1971-0271269-8
S. P. Wang, Compactness properties of topological groups. II, Duke Math. J. 39 (1972), 243–251. MR 296209

Homogeneous spaces with finite invariant volume

L’intégration dans les groupes topologigues

T. S. Wu, A certain type of locally compact totally disconnected topological groups, Proc. Amer. Math. Soc. 23 (1969), 613–614. MR 249537, DOI 10.1090/S0002-9939-1969-0249537-1
T. S. Wu and Y. K. Yu, Compactness properties of topological groups, Michigan Math. J. 19 (1972), 299–313. MR 318391