Stone-Weierstrass theorem


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Stone-Weierstrass theorem

[′stōn ′vī·ər‚sträs ‚thir·əm]
(mathematics)
If S is a collection of continuous real-valued functions on a compact space E, which contains the constant functions, and if for any pair of distinct points x and y in E there is a function ƒ in S such that ƒ(x) is not equal to ƒ(y), then for any continuous real-valued function g on E there is a sequence of functions, each of which can be expressed as a polynomial in the functions of S with real coefficients, that converges uniformly to g.
References in periodicals archive ?
An appendix provides a thorough introduction to measure and integration theory, and additional appendices address the background material on topics such as Zorn's lemma, the Stone-Weierstrass theorem, Tychonoff's theorem on product spaces, and the upper and lower limit points of sequences.