Varieties of abelian topological groups and scattered spaces

Authors

Carolyn E. McPhail, University of WollongongFollow
Sidney A. Morris, University of Ballarat

RIS ID

34516

Publication Details

McPhail, C. E. & Morris, S. A. (2008). Varieties of abelian topological groups and scattered spaces. Australian Mathematical Society. Bulletin, 78 (3), 487-495.

Abstract

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.