Stone-Weierstrass theorem

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Stone-Weierstrass theorem [′stōn ′vī·ər‚sträs ‚thir·əm]

(mathematics)

IfSis a collection of continuous real-valued functions on a compact spaceE, which contains the constant functions, and if for any pair of distinct pointsxandyinEthere is a function ƒ inSsuch that ƒ(x) is not equal to ƒ(y), then for any continuous real-valued functiongonEthere is a sequence of functions, each of which can be expressed as a polynomial in the functions ofSwith real coefficients, that converges uniformly tog.

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