So I'm familiar with the Stone-Weierstrass Theorem for closed intervals [a, b] but am now looking to prove it for a more general 3-dimensional compact set. That is, if f is continuous on the set X, f can be approximated by a polynomial. Any tips to head in that direction? I'm familiar with the long-ish proof involving proving it works on [0, 1] then generalizing.
2026-04-02 01:23:20.1775093000
Example of Stone-Weierstrass Theorem on a non-interval? (3-dim compact set for example)
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