Course Solutions Uncategorized (Solved) : L Thus R Satisfies Hypotheses Theorem 732 Follows Real Continuous Function K Lies Uniform Q32941311 . . . .

(Solved) : L Thus R Satisfies Hypotheses Theorem 732 Follows Real Continuous Function K Lies Uniform Q32941311 . . . .

 

l, it Thus R satisfies the hypotheses of Theorem 7.32. It follows that real continuous function on K lies in the uniform closure of R, lies in B. If f is a complex continuous function on K, f-u+ iv, k valishes at no point of K. U the conclusion xe K, constructed in ets V, containing x, then u E B, ve B, hence fe B. This completes the proof EXERCISES of points x, x 1. Prove that every uniformly convergent sequence of bounded functions is uni- formly bounded. If {f,} and {gal converge uniformly on a 

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