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Characters and Point Evaluations

Published online by Cambridge University Press:  20 November 2018

T. J. Ransford
T. J. Ransford*
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec (Québec) G1K 7P4 e-mail:ransford@mat.ulaval.ca
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Abstract

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We give a simple proof that, if X is a Lindelöf topological space, and A is an algebra of continuous real-valued functions on X which is inverse-closed, local and z-regular, then every character on A is a point evaluation. We also give a number of examples to illustrate both the applications of this theorem and its limitations.

Keywords

46J10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 237 - 241
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. J. Arias-de-Reyna, A real-valued homomorphism on algebras of differentiable functions, Proc. Amer. Math. Soc. 104(1988), 1054–1058.Google Scholar
2. Gillman, L. and Jerison, M., Rings of Continuous Functions, Springer—Verlag, 1976.Google Scholar