Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T07:35:51.770Z Has data issue: false hasContentIssue false
  • English
  • Français

A short elementary proof of the Bishop–Stone–Weierstrass theorem

Published online by Cambridge University Press:  24 October 2008

T. J. Ransford
T. J. Ransford
Affiliation:
Trinity College, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

Fix the following notation. Let X be a compact Hausdorff space, and denote by C(X) the vector space of continuous complex-valued functions on X, equipped with the uniform norm ∥·∥x. Let A be a unital subalgebra of C(X). A non-empty subset S of X is said to be A-antisymmetric if whenever h ∈ A and h is real-valued on S then h is constant on S.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 2 , September 1984 , pp. 309 - 311
Copyright
Copyright © Cambridge Philosophical Society 1984

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.CrossRefGoogle Scholar
[3] Brosowski, B. & Deutsch, F.. An elementary proof of the Stone-Weierstrass theorem. Proc. Amer. Math. Soc. 81 (1981), 89–92.CrossRefGoogle Scholar
[4] Burckel, R. B.. Bishop' Stone-Weierstrass theorem. Amer. Math. Monthly 91 (1984), 22–32.Google Scholar
[5] Glicksberg, I.. Measures orthgonal to algebras and sets of antisymmetry. Trans. Amer. Math. Soc. 105 (1962), 415–435.CrossRefGoogle Scholar
[6] Machado, S.. On Bishop's generalization of the Stone-Weierstrass theorem. Indag. Math. 39 (1977), 218–224.CrossRefGoogle Scholar