Question: a) Let [xn) and {yn} be sequences in X which converge to the same point. Prove that p(xn yn) 0 as n .

a) Let [xn) and {yn} be sequences in X which converge to the same point. Prove that p(xn yn) → 0 as n → ∞.
b) Show that the converse of part a) is false.

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