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Date: 30-7-2021
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Date: 9-8-2021
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If is any compact space, let be a subalgebra of the algebra over the reals with binary operations and . Then, if contains the constant functions and separates the points of (i.e., for any two distinct points and of , there is some function in such that ), is dense in equipped with the uniform norm.
This theorem is a generalization of the Weierstrass approximation theorem.
REFERENCES:
Cullen, H. F. "The Stone-Weierstrass Theorem" and "The Complex Stone-Weierstrass Theorem." In Introduction to General Topology. Boston, MA: Heath, pp. 286-293, 1968.
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