# Stone-Weierstrass theorem

(redirected from*Weierstrass' theorem*)

## 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*.Want to thank TFD for its existence? Tell a friend about us, add a link to this page, or visit the webmaster's page for free fun content.

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