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Note on two theorems about function algebras

Published online by Cambridge University Press:  26 February 2010

R. E. Edwards
R. E. Edwards
Affiliation:
Birkbeck College, London.
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Extract

Let X be a locally compact space, C(X) the algebra (with point-wise operations) of continuous numerical functions on X. On C(X) we introduce the topology of compact convergence. If f ε C(X), Zf denotes the set of zeros of f; and if I is a subset of C(X), we define

Type
Research Article
Information
Mathematika , Volume 4 , Issue 2 , December 1957 , pp. 138 - 139
Copyright
Copyright © University College London 1957

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References

1.Bourbaki, N., Elements de Maihtmatique, Integration, chap. I-IV, Act. Sc. et Ind., No. 1175, Paris (1952).Google Scholar
2.Schwartz, L., Théorie des Distributions, I, Act. Sc. et Ind., No. 1091, Paris (1950).Google Scholar
3.Šilov, G. B., “On regular normed rings”, Trudy Mat. Inst. Steklov, 021 (1947).Google Scholar
4.Šilov, G. E., “Homogeneous rings of functions”, Uspehi Mat. Nauk (N.S.) 6, No. 1(41) (1951); American Math. Soc. Translation, No. 92.Google Scholar
5.Whitney, H., “On ideals of differentiable functions”, American J. Math., 070 (1948), 635–658.CrossRefGoogle Scholar