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A remark on compact semigroups having certain decomposition spaces embeddable in the plane

Published online by Cambridge University Press:  17 April 2009

R. P. Hunter  and
L. W. Anderson
R. P. Hunter
Affiliation:
Pennsylvania State University, University Park, Pennsylvania, USA.
L. W. Anderson
Affiliation:
Pennsylvania State University, University Park, Pennsylvania, USA.
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Abstract

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Let S be a compact connected semigroup. If the decomposition space of S, under the action of a compact connected subgroup at the identity, is a plane continuum then this decomposition is a congruence.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 4 , Issue 1 , February 1971 , pp. 137 - 139
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Anderson, L.W. and Hunter, R.P., “The H-equivalence in compact semigroups”, Bull. Soc. Math. Belg. 14 (1962), 274–296.Google Scholar
[2]Anderson, L.W. and Hunter, R.P., “Compact semigroups having certain one dimensional hyperspaces”, Amer. J. Math. (to appear).Google Scholar
[3]Hofmann, Karl Heinrich and Mostert, Paul S., Elements of compact semigroups (Charles E. Merrill Books, Colombus, Ohio, 1966).Google Scholar
[4]Hunter, R.P., “Certain upper semi-continuous decompositions of a semigroup”, Duke Math. J. 27 (1960), 283–290.CrossRefGoogle Scholar
[5]Hunter, R.P. and Anderson, L.W., “Certain homomorphisms of a compact semigroup onto a thread”, J. Austral. Math. Soc. 7 (1967), 311–322.Google Scholar