Question: Prove that the Bolzano-Weierstrass Property does not hold for C[a, b] and ||f|| (see Example 10.6). Namely, prove that if fn(x) = xn then ||fn||

Prove that the Bolzano-Weierstrass Property does not hold for C[a, b] and ||f|| (see Example 10.6). Namely, prove that if fn(x) = xn then ||fn|| is bounded but ||fnk - f|| does not converge for any f ∈ C[0, 1] and any subsequence {nk}.

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