Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-12-01T07:31:36.312Z Has data issue: false hasContentIssue false
  • English
  • Français

Automorphisms of semigroups of continuous functions

Published online by Cambridge University Press:  09 April 2009

G. R. Wood
G. R. Wood
Affiliation:
Department of Mathematics University of CanterburyChristchurch, New Zealand
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 3 , May 1980 , pp. 301 - 309
Copyright
Copyright © Australian Mathematical Society 1980

References

Cezus, F. A., Magill, K. D. Jr and Subbiah, S. (1975), ‘Maximal ideals of semigroups of endomorphisms’, Bull. Austral. Math. Soc. 12, 211–225.CrossRefGoogle Scholar
Fine, N. J. and Schweigert, G. E. (1955), ‘On the group of homeomorphisms of an arc’, Ann. of Math. 62, 237–253.CrossRefGoogle Scholar
Fitzpatrick, S. P. and Symons, J. S. V. (1975), ‘Automorphisms of transformation semigroups’, Proc. Edinburgh Math. Soc. 19, 327–329.CrossRefGoogle Scholar
Gluskin, L. M. (1959), ‘The semigroup of homeomorphic mappings of an interval’, Mat. Sb. (N.S.) 49 (91), 13–18;Google Scholar
translated in Amer. Math. Soc. Transl. 30, (1963), 273–290.Google Scholar
Gluskin, L. M. (1960), ‘Automorphisms of semigroups of topological mappings’, Izv. Vyss. Ucebn. Zaved. Matematika 6 (19), 62–73;Google Scholar
translated in Amer. Math. Soc. Transl. 36 (1964), 383–395.Google Scholar
Magill, K. D. Jr (1964). ‘Semigroups of continuous functions’, Amer. Math. Monthly 71, 984–988.CrossRefGoogle Scholar
Magill, K. D. Jr (1977), ‘Homomorphisms from g(X) into g(Y)’, Can. J. Math. 29 615–625.CrossRefGoogle Scholar
Schreier, J. (1937), ‘Über Abbildungen einer abstrakten Menge auf ihre Teilmengen’, Fund. Math. 28, 261–264.CrossRefGoogle Scholar
Sullivan, R. P. (1975), ‘Automorphisms of transformation semigroups’, J. Austral. Math. Soc. Ser. A 20, 77–84.CrossRefGoogle Scholar