Compact-like abelian groups without non-trivial quasi-convex null sequences

Details Compact-like abelian groups without non-trivial quasi-convex null sequences Compact-like abelian groups without non-trivial quasi-convex null sequences

2010-07-12

arxiv.org/abs/1007.1927v1

Mathematics

General Topology

First public draft, comments are welcome (17 pages)

Scientific paper

In this paper, we study precompact abelian groups G that contain 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. We characterize groups with this property in the class of totally minimal groups and $\omega$-bounded groups, and obtain a reduction theorem in the class of minimal groups. We also provide examples of minimal abelian groups with this property, and show that under MA or CH there is a countably compact group with the same property.

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