Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T14:16:28.476Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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