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A note on countably compact semigroups

Published online by Cambridge University Press:  09 April 2009

A. Mukherjea  and
N. A. Tserpes
A. Mukherjea
Affiliation:
Department of Mathematics University of South Florida Tampa, Florida, USA
N. A. Tserpes
Affiliation:
Department of Mathematics University of South Florida Tampa, Florida, USA
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It is well known that every compact topological semigroup has an idempotent and every compact bicancellative semigroup is a topological group. Also every locally compact semigroup which is algebraically a group, is a topological group. In this note we extend these results to the case of countably compact semigroups satisfying the Ist axiom of countability. Some of our results are valid under the weaker condition of sequential compactness.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 2 , March 1972 , pp. 180 - 184
Copyright
Copyright © Australian Mathematical Society 1972

References

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