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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
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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