Question: Let C([O, 1]) be the set of continuous functions f : [0, 1] + R. Define the L2 -norm of f by 1/2 Ilf112

Let C([O, 1]) be the set of continuous functions f : [0, 1] + R. Define the L2 -norm of f by 1/2 Ilf112 = (a) Show that the normed linear space (C([O, 1]), II 112) is not complete. (b) Let the LOO -norm of f be defined by Ilflloo for f e C([O, 1]). Show that the normed linear space (C([O, 1]), II 00) is complete.

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