On zero-dimensionality and the connected component of locally pseudocompact groups
arXiv:0909.1390 · doi:10.1090/S0002-9939-2011-10626-9
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.
Paper was completely rewritten since v2, and several new results (Theorems B, C, and D) were added