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VARIETIES OF ABELIAN TOPOLOGICAL GROUPS AND SCATTERED SPACES
Part of
CAROLYN E. MCPHAIL, SIDNEY A. MORRIS
Journal:

Bulletin of the Australian Mathematical Society / Volume 78 / Issue 3 / December 2008

Published online by Cambridge University Press:

01 December 2008, pp. 487-495

Print publication:

December 2008
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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.

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VARIETIES OF ABELIAN TOPOLOGICAL GROUPS AND SCATTERED SPACES