On the quasi-component of pseudocompact abelian groups

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((G) over tilde) of its completion. Specifically, we characterize the pairs (C. A) of compact connected abelian groups C and subgroups A such that A congruent to q(G) and C congruent to q((G) over tilde). 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. (C) 2012 Elsevier B.V. All rights reserved.