The Stone-weierstrass Theorem
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چکیده
The really new thing about Stone’s approach to the approximation theorem was the approach via lattices of continuous functions, although Lebesgue had noticed the importance of approximating the absolute-value function earlier. There is a segment of the mathematical community formed of people who are as likely to encounter a lattice in their work as an algebra and for whom the lattice version of the theorem is at least as important as the algebra version. I’m one of them, but I also thought it more important to expose Stone’s insight (about the density of a lattice with the two-point interpolation property) first.
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