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Semigroup structures for families of functions, II. Continuous functions

Published online by Cambridge University Press:  09 April 2009

Kenneth D. Magill Jr
Kenneth D. Magill Jr
Affiliation:
State University of New York Buffalo
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This is a continuation of [5] and we begin by recalling two definitions and a result of that paper which are needed here. Let be a family of functions with domains contained in a set X and ranges contained in a set Y and let be a function with domain D()= Y and range with the property for each pair of elements ƒ and g of . Since the composition operation is associative, is a semigroup if for ƒ and g in , we define the product ƒg by .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 1 , February 1967 , pp. 95 - 107
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, Mathematical Surveys, Number 7, Amer. Math. Soc. (1961).Google Scholar
[2]de Groot, J., ‘Groups represented by homeomorphism groups I’, Math. Annelen 138 (1959), 80–102.CrossRefGoogle Scholar
[3]Kelley, J. L., General topology, Van Nostrand, Princeton, 1955.Google Scholar
[4]Ljapin, E. S., Semigroups. Translations of Mathematical Monographs, Vol. 3, Amer. Math. Soc., 1963.Google Scholar
[5]Magill, K. D. Jr, ‘Semigroup structures for families of functions, I. Some homomorphism theorems’, Journ. Australian Math. Soc. (to appear).Google Scholar
[6]Springer, G., Introduction to Riemann Surfaces, Addison-Wesley, Reading, Mass., 1957.Google Scholar