On the quasi-component of pseudocompact abelian groups

Details On the quasi-component of pseudocompact abelian groups On the quasi-component of pseudocompact abelian groups

2010-07-24

arxiv.org/abs/1007.4285v3

Topology and its Applications 159 (2012), 2152-2157

Mathematics

General Topology

minor revision

Scientific paper

10.1016/j.topol.2012.02.007

In this paper, we describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component q(\widetilde G) of its completion. Specifically, we characterize the pairs (C,A) of compact connected abelian groups C and subgroups A such that A \cong q(G) and C \cong q(\widetilde G). As a consequence, we show that for every positive integer n or n=\omega, there exist plenty of abelian pseudocompact perfectly minimal n-dimensional groups G such that the quasi-component of G is not dense in the quasi-component of the completion of G.

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