Identifying and distinguishing various varieties of abelian topological groups
- Authors: McPhail, Carolyn , Morris, Sidney
- Date: 2008
- Type: Text , Journal article
- Relation: Dissertationes Mathematicae Vol. , no. 458 (2008), p.
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- Description: 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.
Varieties of abelian topological groups and scattered spaces
- Authors: McPhail, Carolyn , Morris, Sidney
- Date: 2008
- Type: Text , Journal article
- Relation: Bulletin of the Australian Mathematical Society Vol. 78, no. 3 (Dec 2008), p. 487-495
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- Reviewed:
- Description: The variety of topological groups generated by the class of all abelian k(omega)-groups has been shown to equal the variety of topological groups generated by the free abelian topological group on [0, 1]. In this paper it is proved that the free abelian topological group on a compact Hausdorff space X generates the same variety if and only if X is not scattered.