Editing Stone–Weierstrass theorem (section)

== See also ==
*[[Müntz–Szász theorem]]
* [[Bernstein polynomial]]
* [[Runge's phenomenon]] shows that finding a polynomial {{mvar|P}} such that {{math| ''f'' (''x'') {{=}} ''P''(''x'')}} for some finely spaced {{math|''x'' {{=}} ''x<sub>n</sub>''}} is a bad way to attempt to find a polynomial approximating {{math| ''f'' }} uniformly. A better approach, explained e.g. in {{harvtxt|Rudin|1976}}, p. 160, eq. (51) ff., is to construct polynomials {{mvar|P}} uniformly approximating {{math| ''f'' }} by taking the convolution of {{math| ''f'' }} with a family of suitably chosen polynomial kernels.
* [[Mergelyan's theorem]], concerning polynomial approximations of complex functions.