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Date: 20-7-2021
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Date: 15-8-2021
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Date: 25-7-2021
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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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