Unformatted text preview: f uniformly on S and g n → g uniformly on S . Then, 1) Show that, for any real number c , cf n → cf uniformly on S . 2) Show that f n + g n → f + g uniformly on S . Let S = R , f n ( x ) = x , f ( x ) = x , g n ( x ) = 1 /n and g ( x ) = 0. 3) Show that f n g n does not converge to fg uniformly on S. 3. Let S ⊂ R and f, f n : S → R . Suppose f n are all uniformly continuous on S and f n → f uniformly on S . Show that f is uniformly continuous on S . Hint: See the proof of Thm 24.3. 1...
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 Fall '07
 Fukuda
 Calculus, Continuous function, Limit of a function, R. Suppose fn

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