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A short proof of a theorem of Machado

Published online by Cambridge University Press:  24 October 2008

D. A. Edwards
D. A. Edwards
Affiliation:
Mathematical Institute, Oxford
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Extract

Let X be a non-empty compact Hausdorff space and let C(X) denote either the space of all continuous real-valued functions or the space of all complex-valued functions on X, endowed with the norm , where for each non-empty closed F ⊆ X and each f ∈ C(X) we write

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 111 - 114
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Bishop, E.. A generalization of the Stone-Weierstrass Theorem. Pacific J. Math. 11 (1961), 777–783.CrossRefGoogle Scholar
[2]de Branges, L.. The Stone-Weierstrass Theorem. Proc. Amer. Math. Soc. 10 (1959), 822–824.Google Scholar
[3]Browder, A.. Introduction to Function Algebras (Benjamin, 1969).Google Scholar
[4]Burckel, R. B.. Bishop's Stone-Weierstrass Theorem. Amer. Math. Monthly 91 (1984), 22–32.Google Scholar
[5]Gamelin, T. W.. Uniform Algebras (Prentice-Hall, 1969).Google Scholar
[6]Glicksberg, I.. Measures orthogonal to algebras and sets of antisymmetry. Trans. Amer. Amer. Math. Soc. 105 (1962), 415–435.Google Scholar
[7]Leibowitz, G. M.. Lectures on Complex Function Algebras (Scott, Foresman & Co., 1970).Google Scholar
[8]Machado, S.. On Bishop's generalization of the Stone-Weierstrass Theorem. Indag. Math. 39 (1977), 218–224.CrossRefGoogle Scholar
[9]Ransford, T. J.. A short elementary proof of the Bishop-Stone-Weierstrass Theorem. Math. Proc. Cambridge Philos. Soc. 96 (1984), 309–311.CrossRefGoogle Scholar