English

Linear topologies on $\Z$ are not Mackey topologies

General Topology 2011-09-02 v2 Group Theory

Abstract

In this article it is shown that to every non-discrete Hausdorff linear topology on Z\Z other metrizable locally quasi-convex group topologies can be associated which are strictly finer than the linear topology and such that the character groups coincide. Applying this result to the pp-adic topology on Z\Z, we give a negative answer to the question of Dikranjan, whether this topology is Mackey.

Cite

@article{arxiv.1107.2661,
  title  = {Linear topologies on $\Z$ are not Mackey topologies},
  author = {Lydia Aussenhofer and Daniel de la Barrera Mayoral},
  journal= {arXiv preprint arXiv:1107.2661},
  year   = {2011}
}

Comments

9 pages

R2 v1 2026-06-21T18:36:22.853Z