If G = (G, τ) is a topological group with topology τ, then there is a smallest topology τ* ⊇ τ such that G* = (G, τ*) is a topological group with equal left and right uniformities (1). Bagley and Wu introduced this topology in (1), and studied the relationship between Gand G*. In this paper we prove some additional results concerning G* and groups with equal uniformities in general. The structure of locally compact groups with equal uniformities has been studied extensively. If G is a locally compact connected group, then G has equal uniformities if and only if G ≅ V× K,where F is a vector group and Kis a compact group (5). More generally, every locally compact group with equal uniformities has an open normal subgroup of the form V× K(4).
@article{10_4153_CJM_1969_074_8,
author = {Ramsay, R. T.},
title = {Groups with {Equal} {Uniformities}},
journal = {Canadian journal of mathematics},
pages = {655--659},
year = {1969},
volume = {21},
number = {1},
doi = {10.4153/CJM-1969-074-8},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-074-8/}
}
TY - JOUR
AU - Ramsay, R. T.
TI - Groups with Equal Uniformities
JO - Canadian journal of mathematics
PY - 1969
SP - 655
EP - 659
VL - 21
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-074-8/
DO - 10.4153/CJM-1969-074-8
ID - 10_4153_CJM_1969_074_8
ER -
%0 Journal Article
%A Ramsay, R. T.
%T Groups with Equal Uniformities
%J Canadian journal of mathematics
%D 1969
%P 655-659
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-074-8/
%R 10.4153/CJM-1969-074-8
%F 10_4153_CJM_1969_074_8
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