Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-01T02:49:55.950Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuous nilpotents on topological spaces

Part of: Maps and general types of spaces defined by maps Semigroups

Published online by Cambridge University Press:  09 April 2009

R. P. Sullivan  and
J. H. Rubinstein
R. P. Sullivan
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, 6009, Australia
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.

K. D. Magill has investigated the semigroup generated by the idempotent continuous mappings of a topological space into itself and examined whether this semigroup determines the space to within homeomorphism. By analogy with this (and related work of Bridget Bos Baird) we now consider the semigroup generated by nilpotent continuous partial mappings of a space into itself.

Keywords

semigroupcontinuous mappingstopological spaceisomorphism

MSC classification

Secondary: 54C05: Continuous maps 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 1 , August 1987 , pp. 127 - 136
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Baird, B. B., ‘Isomorphisms between inverse semigroups of injective transformations,’ J. Austral. Math. Soc. (Series A) 23 (1977), 194–201.CrossRefGoogle Scholar
[2]Howie, J. M., ‘The subsemigroup generated by the idempotents of a full transformation semigroup’, J. London Math. Soc. 41 (1966), 707–716.CrossRefGoogle Scholar
[3]Kuratowski, K., Topology, Vol. 1 (Academic Press, New York, 1966).Google Scholar
[4]Magill, K. D. Jr., ‘Semigroups of functions generated by idempotents’, J. London Math. Soc. 44 (1969), 236–242.CrossRefGoogle Scholar
[5]Magill, K. D. Jr., ‘Homomorphisms from S(X) onto S(Y)’, Canad. J. Math. 29 (1977), 615–625.CrossRefGoogle Scholar
[6]Sullivan, R. P., ‘Automorphisms of transformation semigroups’, J. Austral. Math. Soc. (Series A) 20 (1975), 77–84.CrossRefGoogle Scholar
[7]Sullivan, R. P., ‘Semigroups generated by nilpotent transformations’, submitted.Google Scholar
[8]Wood, G. R., ‘Automorphisms of semigroups of continuous functions’, J. Austral. Math. Soc. (Series A) 29 (1980), 301–309.CrossRefGoogle Scholar