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Restrictive Semigroups of Closed Functions

Published online by Cambridge University Press:  20 November 2018

Kenneth D. Magill JR.
Kenneth D. Magill JR.*
Affiliation:
State University of New York, Buffalo, New York
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It is assumed that all topological spaces discussed in this paper are T1 spaces. A function ƒ mapping a topological space X into itself is a closed function if ƒ[H] is closed for each closed subset H of S. The semigroup, under composition, of all closed functions mapping X into X is denoted by Γ(X). These were among the semigroups under consideration in (4).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1215 - 1229
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Math. Surveys, Number 7 (Amer. Math. Soc, Providence, R.I., 1961).Google Scholar
2. Gillman, L. and Jerison, M., Rings of continuous functions (Van Nostrand, New York, 1960).10.1007/978-1-4615-7819-2CrossRefGoogle Scholar
3. Ljapin, E. S., Semigroups, Translations of Mathematical Monographs, Vol. 3 (Amer. Math. Soc, Providence, R.I., 1963).Google Scholar
4. Magill, K. D., Jr., Semigroups of functions on topological spaces, Proc. London Math. Soc. 3) 16 (1966), 507–518.Google Scholar
5. Magill, K. D., Jr., Subsemigroups of S(X), Math. Japon. 11 (1966), 109–115.Google Scholar
6. Vitanza, M. L., Mappings of semigroups associated with ordered pairs, Amer. Math. Monthly 73 (1966), 1078–1082.Google Scholar