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Homomorphic images of restrictive star semigroups

Published online by Cambridge University Press:  18 May 2009

Kenneth D. Magill Jr
Kenneth D. Magill Jr
Affiliation:
State University of New York at Buffalo, and University of Leeds
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Let Y be a subspace of a topological space X. Then S(X, Y) denotes the semigroup, under composition, of all continuous selfmaps of X which also carry Y into Y. In the special case Y = X, the simpler notation S(X)is used. We have devoted several recent papers ([4], [7] and [8]) to the problem of determining when S(Z) and S(X, Y)are isomorphic and, more generally, when S(Z) is a homomorphic image of S(X, Y). In this paper, we investigate the analogous problem for certain semigroups of functions on spaces which were introduced in [5]. These include semigroups of closed functions which are treated in further detail.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 11 , Issue 1 , January 1970 , pp. 58 - 71
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

REFERENCES

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