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Varieties of abelian topological groups and scattered spaces

Journal Article


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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.

Publication Date


  • 2008

Citation


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

Scopus Eid


  • 2-s2.0-77957225904

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=9935&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2599

Number Of Pages


  • 8

Start Page


  • 487

End Page


  • 495

Volume


  • 78

Issue


  • 3

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.

Publication Date


  • 2008

Citation


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

Scopus Eid


  • 2-s2.0-77957225904

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=9935&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/2599

Number Of Pages


  • 8

Start Page


  • 487

End Page


  • 495

Volume


  • 78

Issue


  • 3