Stone-Weierstrass theorem

Let X be a compact space and let C0(X,) be the algebra of continuousPlanetmathPlanetmath real functions defined over X. Let 𝒜 be a subalgebra of C0(X,) for which the following conditions hold:

  1. 1.


  2. 2.


Then 𝒜 is dense in C0(X,).

This theorem is a generalizationPlanetmathPlanetmath of the classical Weierstrass approximation theoremMathworldPlanetmath to general spaces.

Title Stone-Weierstrass theorem
Canonical name StoneWeierstrassTheorem
Date of creation 2013-03-22 12:42:06
Last modified on 2013-03-22 12:42:06
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 9
Author rspuzio (6075)
Entry type Theorem
Classification msc 46E15