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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
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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

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References

REFERENCES

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