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Homomorphisms from S(X) into S(Y)

Published online by Cambridge University Press:  20 November 2018

Kenneth D. Magill
Kenneth D. Magill*
Affiliation:
State University of New York at Buffalo, Amherst, New York
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Abstract

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S(X) is the semigroup under composition of all continuous selfmaps of the topological space X. For certain spaces X and Y we classify completely the homomorphisms from S(X) into S(Y). An application of the main result to S(I) the semigroup of all continuous selfmaps of the closed unit interval I results in the solution of a problem which was suggested in the closing paragraph of [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 3 , 01 June 1977 , pp. 615 - 625
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Gluskin, L. M., The semigroup of all homeomorphic mappings of an interval, Mat. Sb. (N.S.) 1+9 (91) (1959), 13–18.Google Scholar
2. Gluskin, L. M. The semigroup of homeomorphic mappings of an interval, Amer. Math. Soc. Transi. (20) SO(1963), 273–290.Google Scholar
3. Magill, K. D., Jr., Subgroups of semigroups of functions, Port. Math. 26 (1967), 133–147.Google Scholar
4. Magill, K. D. Topological spaces determined by left ideals of semigroups, Pac. Math. J. (2) 24 (1968), 319–330.Google Scholar
5. Magill, K. D. Semigroups which admit few embeddings, Fund. Math. 85 (1974), 37–53.Google Scholar
6. Magill, K. D. A survey of embedding theorems for semigroups of continuous functions, Studies in Topology, edited by N. M. Stavrakas and K. R. Allen (Academic Press, New York, 1975).Google Scholar
7. Magill, K. D. A survey of semigroups of continuous self maps, Semigroup Forum, (11) 3 (1975/76) 189–282.Google Scholar
8. Whyburn, G. T., Analytic topology (AMS Colloquium Publication 28, New York, 1942).Google Scholar