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VARIETIES OF ABELIAN TOPOLOGICAL GROUPS AND SCATTERED SPACES

Part of: Abelian groups Peculiar spaces Topological and differentiable algebraic systems Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  01 December 2008

CAROLYN E. MCPHAIL  and
SIDNEY A. MORRIS
CAROLYN E. MCPHAIL
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia (email: sandison@uow.edu.au)
SIDNEY A. MORRIS*
Affiliation:
School of Information Technology and Mathematical Sciences, University of Ballarat, PO Box 663, Ballarat, VIC 3353, Australia (email: s.morris@ballarat.edu.au)
*
✉For correspondence; e-mail: s.morris@ballarat.edu.au
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Abstract

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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.

Keywords

variety of topological groupsabelian topological groupscattered topological spacefree abelian topological group[0,1]Peano curve

MSC classification

Secondary: 22A05: Structure of general topological groups 20E10: Quasivarieties and varieties of groups 20K99: None of the above, but in this section 54G12: Scattered spaces
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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