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 ˜ ) of its completion. Specifically, we characterize the pairs ( C , A ) of compact connected abelian groups C and subgroups A such that A ≅ q ( G ) and C ≅ q ( G ˜ ) . As a consequence, we show that for every positive integer n or n = ω , 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.