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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

[1]Berglund, J. F. and Hofmann, K. H., Compact semitopological semigroups and weakly almost periodic functions (Springer, New York, 1967, Lecture Notes in Math. No. 42).CrossRefGoogle Scholar
[2]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups Vol. I, II (Amer. Math. Society, 1961, 1967).Google Scholar
[3]Dugundji, J., Topology (Allyn and Bacon, Boston, 1966).Google Scholar
[4]Gelbaum, B., Kalisch, G. K. and Olmsted, J. M. H., ‘On the embedding of topological semigroups and integral domains’, Proc. Amer. Math. Soc. 2 (1951), 807–821.CrossRefGoogle Scholar
[5]Kelley, J. L., General Topology (Van Nostrand, New York, 1955).Google Scholar
[6]Koch, R. J. and Wallace, A. D., ‘Maximal ideals in topological semigroups’, Duke Math. J. 21 (1954), 681–685.CrossRefGoogle Scholar
[7]Morita, K. and Hanai, S., ‘Closed mappings and metric spaces’, Proc. Jap. Acad. 32 (1956), 10–14.Google Scholar
[8]Numakura, K., ‘On bicompact semigroups’, Math. J. Okayama Univ. 1 (1955), 99–108.Google Scholar
[9]Wallace, A. D., ‘The structure of topological semigroups’, Amer. Math. Soc. Bull. 61 (1955), 95–112.CrossRefGoogle Scholar