ar X iv : 0 90 1 . 01 32 v 1 [ m at h . G N ] 3 1 D ec 2 00 8 Locally compact abelian groups admitting non - trivial quasi - convex null sequences
نویسنده
چکیده
In this paper, we show that for every locally compact abelian group G, the following statements are equivalent: (i) G contains no sequence {xn}n=0 such that {0} ∪ {±xn | n ∈ N} is infinite and quasiconvex in G, and xn −→ 0; (ii) one of the subgroups {g ∈ G | 2g = 0} and {g ∈ G | 3g = 0} is open in G; (iii) G contains an open compact subgroup of the form Z2 or Z κ 3 for some cardinal κ.
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تاریخ انتشار 2008