y**t
发帖数: 50 | 1 I dunno which version of stone-w theorem you know
the one I know is that if A contains a nonzero
constant function,then A is dense in C(X).And if you
know the proof of the s-w theorem,it should not be
hard for you to prove this exercise.
Use contradiction to prove that there is a point p
in X such that any f in A f(p)=0 if A is not dense
in C(X).if any point x in X there is a function such that
f(x)!=0then f!=0 in a neiborhood of x,using compactness
you can find f1 through fl such that f=f1^2+.. |
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