Topological groups: local versus global

A. V. Arhangelskii; Vladimir V. Uspenskij

doi:10.4995/agt.2006.1933

Authors

A. V. Arhangelskii Ohio University
Vladimir V. Uspenskij Ohio University

DOI:

https://doi.org/10.4995/agt.2006.1933

Keywords:

Topological group, Paracompact, Lindelöf, Local properties

Abstract

It is well known that locally compact groups are paracompact. We observe that this theorem can be generalized as follows: every locally paracompact group is paracompact. We prove a more general version of this statement using quotients. Similar ‘local implies global’ theorems hold also for many other properties, such as normality, metacompactness, stratifiability, etc.

Downloads

Download data is not yet available.

Author Biographies

A. V. Arhangelskii, Ohio University

Department of Mathematics

Vladimir V. Uspenskij, Ohio University

Department of Mathematics

References

A. V. Arhangel'skii, Classes of topological groups, Russian Math. Surveys 36:3 (1981), 151-174. https://doi.org/10.1070/RM1981v036n03ABEH004249

A. V. Arhangel'skii, Quotients with respect to locally compact subgroups, submitted, December 2002.

R. Engelking, General Topology (PWN, Warszawa, 1977).

I. Guran, On topological groups close to being Lindelof, Soviet Math. Dokl. 23 (1981), 173-175.

A. Mysior, A union of realcompact spaces, Bull. Acad. Polon. Sci. Ser. Sci. Math. 29 (1981), no. 3-4, 169-172.

V. Pestov, Topological groups: Where to from here?, Topology Proc. 24 (1999), 421-502. E-print: math.GN/9910144

J.-P. Serre, Compacité locale des espaces fibré, C. R. Acad. Paris 229 (1949), 1295-1297. [=OEuvres, vol. 1]

V. V. Uspenskij, Why compact groups are dyadic, in: General Topology and its relations to modern analysis and algebra VI: Proc. of the 6th Prague topological Symposium 1986, edited by Z. Frolik (Heldermann, Berlin, 1988), 601-610.