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Countably infinite quasi-convex sets in some locally compact abelian groups |
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| Authors: | Dikran Dikranjan |
| Institution: | a Department of Mathematics and Computer Science, University of Udine, Via delle Scienze, 208, Loc. Rizzi, 33100 Udine, Italy b Department of Geometry and Topology, Faculty of Mathematics, Complutense University, Plaza de Ciencias, 3, 28040 Madrid, Spain |
| Abstract: | We produce a class of countably infinite quasi-convex sets (sequences converging to zero) in the circle group T and in the group J2 of 2-adic integers determined by sequences of integers satisfying a mild lacunarity condition. We also extend our results to the group R of real numbers. All these quasi-convex sets have a stronger property: Every infinite (necessarily) symmetric subset containing 0 is still quasi-convex. |
| Keywords: | primary 22A05 secondary 22B05 |
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