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 -groups; (iii) the class of all σ-compact groups; and (iv) the free abelian topological group on [0,1]. In all cases, hierarchical containments are determined.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm458-0-1,
author = {Carolyn E. McPhail and Sidney A. Morris},
title = {Identifying and distinguishing various varieties of abelian topological groups},
series = {GDML\_Books},
year = {2008},
zbl = {1155.22003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm458-0-1}
}
Carolyn E. McPhail; Sidney A. Morris. Identifying and distinguishing various varieties of abelian topological groups. GDML_Books (2008), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm458-0-1/