Locally compact abelian groups admitting non-trivial quasi-convex null sequences

Details Locally compact abelian groups admitting non-trivial quasi-convex null sequences Locally compact abelian groups admitting non-trivial quasi-convex null sequences

2008-12-31

arxiv.org/abs/0901.0132v1

Mathematics

General Topology

18 pages

Scientific paper

In this paper, we show that for every locally compact abelian group G, the following statements are equivalent: (i) G contains no sequence {x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0; (ii) one of the subgroups {g \in G : 2g=0 and {g \in G : 3g=0} is open in G; (iii) G contains an open compact subgroup of the form Z_2^\kappa or Z_3^\kappa for some cardinal \kappa.

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