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Two-part question on a finite dimensional normed linear space

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1 Suppose that  is a finite dimensional normed linear space.
a) Let be a basis for . Define Prove that 1, the closed unit ball in , is compact in (, )
b) Prove that any two norms on  are equivalent.

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This solution is comprised of a detailed explanation to prove the functions. The two norms of equivalents are proved.

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1 Suppose that  is a finite dimensional normed linear space.
a) Let ...

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