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Maximal inverse subsemigroups of S(X)
Published online by Cambridge University Press: 18 May 2009
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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).
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- Copyright © Glasgow Mathematical Journal Trust 1983
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