Identifying and distinguishing various varieties of abelian topological groups

Carolyn E. McPhail, and Sidney A. Morris. Identifying and distinguishing various varieties of abelian topological groups. 2008. <http://eudml.org/doc/285981>.

@book{CarolynE2008,
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 $k_\{ω\}$-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.},
author = {Carolyn E. McPhail, Sidney A. Morris},
keywords = {(abelian) topological group; (wide) variety of topological groups; locally compact abelian group; (locally)-compact abelian group; separable abelian group; free abelian group; groups},
language = {eng},
title = {Identifying and distinguishing various varieties of abelian topological groups},
url = {http://eudml.org/doc/285981},
year = {2008},
}

TY - BOOK
AU - Carolyn E. McPhail
AU - Sidney A. Morris
TI - Identifying and distinguishing various varieties of abelian topological groups
PY - 2008
AB - 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 $k_{ω}$-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.
LA - eng
KW - (abelian) topological group; (wide) variety of topological groups; locally compact abelian group; (locally)-compact abelian group; separable abelian group; free abelian group; groups
UR - http://eudml.org/doc/285981
ER -