Important metric spaces. Fix p = [1, ∞). Let lº denote the collection of all sequences {n}neN in R such that EnEN XnP < x; i.e. M:= {traher:x {n}neNnER Vn, [leal" <0} nEN Define dp P x P → [0, ∞x) as 1/p - (1 1). |xn - Yn | P nEN dp({n}neN, {n}nEN) = (i) Prove that (lP, dp) is a metric space. Note. You can read about this result from various references. (ii) Is P compact? Support your answer with a proof. (iii) Prove that is separable.

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