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Identifying and distinguishing various varieties of abelian topological groups

Journal Article


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.

Publication Date


  • 2008

Citation


  • McPhail, C. E. & Morris, S. A. (2008). Identifying and distinguishing various varieties of abelian topological groups. Dissertationes Mathematicae, 458 1-45.

Scopus Eid


  • 2-s2.0-84858765907

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2600

Number Of Pages


  • 44

Start Page


  • 1

End Page


  • 45

Volume


  • 458

Place Of Publication


  • http://journals.impan.pl

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.

Publication Date


  • 2008

Citation


  • McPhail, C. E. & Morris, S. A. (2008). Identifying and distinguishing various varieties of abelian topological groups. Dissertationes Mathematicae, 458 1-45.

Scopus Eid


  • 2-s2.0-84858765907

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2600

Number Of Pages


  • 44

Start Page


  • 1

End Page


  • 45

Volume


  • 458

Place Of Publication


  • http://journals.impan.pl