On zero-dimensionality and the connected component of locally pseudocompact groups
General Topology
2011-09-27 v3 Group Theory
Abstract
A topological group is locally pseudocompact if it contains a non-empty open set with pseudocompact closure. In this note, we prove that if G is a group with the property that every closed subgroup of G is locally pseudocompact, then G_0 is dense in the component of the completion of G, and G/G_0 is zero-dimensional. We also provide examples of hereditarily disconnected pseudocompact groups with strong minimality properties of arbitrarily large dimension, and thus show that G/G_0 may fail to be zero-dimensional even for totally minimal pseudocompact groups.
Cite
@article{arxiv.0909.1390,
title = {On zero-dimensionality and the connected component of locally pseudocompact groups},
author = {Dikran Dikranjan and Gábor Lukács},
journal= {arXiv preprint arXiv:0909.1390},
year = {2011}
}
Comments
Paper was completely rewritten since v2, and several new results (Theorems B, C, and D) were added