Posted by J. Holmer on September 11, 2007, 9:18 pm, in reply to "HW2 problem2(a)" || f || = \sup_{a<= x<=b} |f(x)| This makes C[a,b] into a complete normed vector space, and hence a metric space.
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The metric on C[a,b] is \rho(f,g) = || f-g ||, where || . || is the supremum norm. 112
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