In this post we will use the Krein–Milman theorem together with the Hahn–Banach theorem to give another proof of the Stone–Weierstrass theorem. The proof we present does not make use of the classical Weierstrass approximation theorem, so we will have here an alternative proof of the classical theorem as well.
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Functional Analysis – Introduction. Part II
In a previous post we discussed some of the history of functional analysis and we also said some vague things about its role in mathematics. In this second part of the introduction we will see an example of the spirit of functional analysis in action, by taking a close look at the Stone-Weierstrass approximation theorem.
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