作者
Karl Heinrich Hofmann, Sidney A Morris
发表日期
1990/11/30
期刊
Journal of Pure and Applied Algebra
卷号
68
期号
1-2
页码范围
181-194
出版商
North-Holland
简介
We show that every locally compact group G contains a discrete subspace X which is closed in G⧹{1} and has the property that G is the smallest closed subgroup containing X. The minimum of the set of all cardinals card X for these X is called the generating rank s (G) of G. We show that s (G)≤ w (G)≤ s (G) ℵ 0 for all G which are not monothetic. We calculate s (G) for G with w (G)≤ c. For compact groups G with w (G)≤ c and finitely many components, s (G) is finite.
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