Minimality Conditions in Topological Groups

Dikran Dikranjan () and Michael Megrelishvili ()
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Dikran Dikranjan: Udine University, Department of Mathematics
Michael Megrelishvili: Bar-Ilan University, Department of Mathematics

A chapter in Recent Progress in General Topology III, 2014, pp 229-327 from Springer

Abstract: Abstract This is a survey on the recent progress in minimal topological groups, with a particular emphasis on constructions leading to non-abelian minimal groups, as semidirect products, generalized Heisenberg groups and other groups naturally arising in Analysis and Geometry. A special attention is paid to several generalizations of minimality (as local minimality, relative minimality and co-minimality), the relations of minimality to (dis)connectedness and to various level of compactness and completeness.

Keywords: Minimal Abelian Group; Generalized Heisenberg Groups; Pseudocompact Group; Paratopological Group; Countably Compact Group (search for similar items in EconPapers)
Date: 2014
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DOI: 10.2991/978-94-6239-024-9_6

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