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Automorphisms of semigroups of continuous functions

  • G. R. Wood (a1)

Abstract

Certain semigroups of continuous selfmaps of the closed unit interval are shown to have the property that all their automorphisms are inner. Contrary to expectation, certain other such semigroups do have outer automorphisms.

1980 Mathematics subject classification (Amer. Math. Soc.): primary 20 M 20; secondary 54 C 40.

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References

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Cezus, F. A., Magill, K. D. Jr and Subbiah, S. (1975), ‘Maximal ideals of semigroups of endomorphisms’, Bull. Austral. Math. Soc. 12, 211225.
Fine, N. J. and Schweigert, G. E. (1955), ‘On the group of homeomorphisms of an arc’, Ann. of Math. 62, 237253.
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translated in Amer. Math. Soc. Transl. 30, (1963), 273290.
Gluskin, L. M. (1960), ‘Automorphisms of semigroups of topological mappings’, Izv. Vyss. Ucebn. Zaved. Matematika 6 (19), 6273;
translated in Amer. Math. Soc. Transl. 36 (1964), 383395.
Magill, K. D. Jr (1964). ‘Semigroups of continuous functions’, Amer. Math. Monthly 71, 984988.
Magill, K. D. Jr (1977), ‘Homomorphisms from g(X) into g(Y)’, Can. J. Math. 29 615625.
Schreier, J. (1937), ‘Über Abbildungen einer abstrakten Menge auf ihre Teilmengen’, Fund. Math. 28, 261264.
Sullivan, R. P. (1975), ‘Automorphisms of transformation semigroups’, J. Austral. Math. Soc. Ser. A 20, 7784.
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