Building suitable sets for locally compact groups by means of continuous selections

被引：2

作者：

Shakhmatov, Dmitri ^{[1
]}

机构：

[1] Ehime Univ, Grad Sch Sci & Engn, Div Math Phys & Earth Sci, Matsuyama, Ehime 7908577, Japan

来源：

TOPOLOGY AND ITS APPLICATIONS | 2009年 / 156卷 / 07期

关键词：

Locally compact group; Generating rank; Suitable set; Lower semicontinuous; Set-valued map; Selection; Converging sequence; Compactly generated; WEIGHT;

D O I：

10.1016/j.topol.2008.12.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

If a discrete subset S of a topological group G with the identity I generates a dense subgroup of G and S boolean OR (1) is closed in G, then S is called a suitable set for G. We apply Michael's selection theorem to offer a direct, self-contained, purely topological proof of the result of Hofmann and Morris [K.-H. Hofmann, S.A. Morris, Weight and c, J. Pure Appl. Algebra 68 (1-2) (1990) 181-194] on the existence of suitable sets in locally compact groups. Our approach uses only elementary facts from (topological) group theory. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：1216 / 1223

页数：8

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