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Two semigroups of continuous relations

Published online by Cambridge University Press:  09 April 2009

A. R. Bednarek  and
Eugene M. Norris
A. R. Bednarek
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32601, U.S.A.
Eugene M. Norris
Affiliation:
Department of Mathematics and Computer Science, University of South Carolina, Columbia, South Carolina 29208, U.S.A.
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Synopsis

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In this paper we define two semigroups of continuous relations on topological spaces and determine a large class of spaces for which Banach-Stone type theorems hold, i.e. spaces for which isomorphism of the semigroups implies homeomorphism of the spaces. This class includes all 0-dimensional Hausdorff spaces and all those completely regular Hausdorff spaces which contain an arc; indeed all of K. D. Magill's S*-spaces are included. Some of the algebraic structure of the semigroup of all continuous relations is elucidated and a method for producing examples of topological semigroups of relations is discussed.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1977 , pp. 46 - 58
Copyright
Copyright © Australian Mathematical Society 1977

References

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