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Automorphism groups of sandwich semigroups

Part of: Semigroups

Published online by Cambridge University Press:  26 February 2010

K. D. Magill Jr
K. D. Magill Jr
Affiliation:
Department of Mathematics, 106 Diefendorf Hall, SUNY at Buffalo, Buffalo, New York 14214-3093, U.S.A.
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Extract

Sandwich semigroups were introduced in [4], [5] and [6]. Green's relations (for regular elements) were characterized for these semigroups in [11] and [13]. Sandwich semigroups of continuous functions first made their appearance in [5]. In this paper, we consider only sandwich semigroups of continuous functions and we refer to them simply as sandwich semigroups. We now recall the definition. Let X and Y be topological spaces and fix a continuous function α from Y into X. Let S(X, Y, α) denote the semigroup of all continuous functions from X into Y where the product fg of f, g ε S(X, Y, α) is defined by fg = f ∘ α ∘ g. We refer to S(X, Y, α) as a sandwich semigroup with sandwich function α. If X = Y and α is the identity map then S(X, Y, α) is, of course, just S(X), the semigroup of all continuous selfmaps of X.

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Mathematika , Volume 34 , Issue 1 , June 1987 , pp. 19 - 28
Copyright
Copyright © University College London 1987

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References

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