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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
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
Copyright
Copyright © Australian Mathematical Society 1967

References

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[6]Springer, G., Introduction to Riemann Surfaces, Addison-Wesley, Reading, Mass., 1957.Google Scholar