查看文章

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.