Question: Problem 6 On the square X = [0, 1] x [0, 1] define the metric d by the formula == 1o it gy=a d{er, ),

Problem 6 On the square X = [0, 1] x [0, 1] define the metric d by the formula == 1o it gy=a d{er, ), (Eapa)) = 8 = 1 otherwise (1) Show that d is indeed a metric. (2) Prove that X is a complete metric space. (3) Is X totally bounded? (4) Is it true that the topology on X given by d is the same as the order topology coming from the lexicographic order on [0, 1] x [0, 1]

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