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Generating varieties of topological groups

Published online by Cambridge University Press:  20 January 2009

M. S. Brooks ,
Sidney. A. Morris  and
Stephen. A. Saxon
M. S. Brooks
Affiliation:
Canberra College of Advanced Education, Canberra, A.C.T., 2600, Australia
Sidney. A. Morris
Affiliation:
University of New South Wales, Kensington, N.S.W., 2033, Australia
Stephen. A. Saxon
Affiliation:
University of Florida, Gainesville, Florida, 32601, U.S.A.
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Recently several papers on varieties of topological groups have appeared. In this note we investigate the question: if Ω is a class of topological groups, what topological groups are in the variety V(Ω) generated by Ω that is, what topological groups can be “manufactured” from Ω using repeatedly the operations of taking subgroups, quotient groups and arbitrary cartesian products? We seeka general theorem which will be useful for investigating V(Ω) for well-known classesΩ.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 3 , June 1973 , pp. 191 - 197
Copyright
Copyright © Edinburgh Mathematical Society 1973

References

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