Identifying and distinguishing various varieties of abelian topological groups
Volume 458 / 2008
Dissertationes Mathematicae 458 (2008), 1-45
MSC: 22A05, 20E10, 54D35, 54D50.
DOI: 10.4064/dm458-0-1
Abstract
A variety of topological groups is a class of (not necessarily Hausdorff) topological groups closed under the operations of forming subgroups, quotient groups and arbitrary products. The variety of topological groups generated by a class of topological groups is the smallest variety containing the class. In this paper methods are presented to distinguish a number of significant varieties of abelian topological groups, including the varieties generated by (i) the class of all locally compact abelian groups; (ii) the class of all $k_\omega$-groups; (iii) the class of all $\sigma$-compact groups; and (iv) the free abelian topological group on $[0,1]$. In all cases, hierarchical containments are determined.
