On zero-dimensionality and the connected component of locally pseudocompact groups

Details On zero-dimensionality and the connected component of locally pseudocompact groups On zero-dimensionality and the connected component of locally pseudocompact groups

2009-09-08

arxiv.org/abs/0909.1390v3

Proceedings of the American Mathematical Society, 139 (2011), no. 8, 2995--3008

Mathematics

General Topology

Paper was completely rewritten since v2, and several new results (Theorems B, C, and D) were added

Scientific paper

10.1090/S0002-9939-2011-10626-9

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.

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