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VARIETIES OF ABELIAN TOPOLOGICAL GROUPS AND SCATTERED SPACES
Published online by Cambridge University Press: 01 December 2008
Abstract
The variety of topological groups generated by the class of all abelian kω-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.
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- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 78 , Issue 3 , December 2008 , pp. 487 - 495
- Copyright
- Copyright © 2009 Australian Mathematical Society
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