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Maximal inverse subsemigroups of S(X)

Published online by Cambridge University Press:  18 May 2009

Bridget B. Baird
Bridget B. Baird
Affiliation:
Department of Mathematics University of Florida Gainesville, Florida 32611
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If X is a topological space then S(X) will denote the semigroup, under composition, of all continuous functions from X into X. An element f in a semigroup is regular if there is an element g such that fgf = f. The regular elements of S(X) will be denoted by R(X). Elements f and g are inverses of each other if fgf = f and gfg = g. Every regular element has an inverse [1]. If every element in a semigroup has a unique inverse then the semigroup is an inverse semigroup. In this paper we examine maximal inverse subsemigroups of S(X).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 24 , Issue 1 , January 1983 , pp. 53 - 64
Copyright
Copyright © Glasgow Mathematical Journal Trust 1983

References

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