Question: 7. (3) Let S1(0) = {r L2(0, 1)|||| = 1}. Prove that S1(0) is closed. Prove that a continuous (not necessarily linear) function f

7. (3) Let S1(0) = {r L2(0, 1)|||| = 1}. Prove that S1(0) is closed. Prove that a continuous (not necessarily linear) function f

7. (3) Let S1(0) = {r L2(0, 1)|||| = 1}. Prove that S1(0) is closed. Prove that a continuous (not necessarily linear) function f : S1(0) R does not necessarily achieve its minimum on Si(0), i.e., that min-eS, (0) (x) may not exist.

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