On the quasi-component of pseudocompact abelian groups

DOI10.1016/J.TOPOL.2012.02.007zbMATH Open1238.22002arXiv1007.4285OpenAlexW2044480287MaRDI QIDQ411817

Gábor Lukács, Dikran Dikranjan

Publication date: 30 April 2012

Published in: Topology and its Applications (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1007.4285

zbMATH Keywords

zero-dimensionalcompletiongroupminimalessentialpseudocompactprecompactperfectly minimalperfectly totally minimalquasi-componenttotally minimal

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Compactness (54D30) Topological groups (topological aspects) (54H11) ``(P)-minimal and ``(P)-closed spaces (54D25) Compact groups (22C05) Connected and locally connected spaces (general aspects) (54D05)

Cites Work

• Sections in principal fibre spaces
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