- Title
- Identifying and distinguishing various varieties of abelian topological groups
- Creator
- McPhail, Carolyn; Morris, Sidney
- Date
- 2008
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/39874
- Identifier
- vital:1791
- Identifier
- ISSN:0012-3862
- Identifier
-
https://doi.org/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(w)-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.
- Publisher
- Polish Academy Sciences Institute Mathematics
- Relation
- Dissertationes Mathematicae Vol. , no. 458 (2008), p.
- Rights
- Copyright Polish Academy Sciences Institute Mathematics
- Rights
- This metadata is freely available under a CCO license
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