Question: Exercise 4 ( 6 points ) . Let ( * 1 , di ) . .... ( * n , An ) be metric spaces

Exercise 4 ( 6 points ) . Let ( * 1 , di ) . .... ( * n , An ) be metric spaces and let * _ _ Xi. Equip I with a metric the way seen in class . Let ( ack ) & C X. For all KE N we can write ack ( OCK, 1 , *Ck, 2 1 ... . 2 kin ) , where for each it [ ] . .... ~' the number ack.; E X; is the ith coordinate of ack` Let a = ( a1 , 02 . ... . an ) EX. Prove that limk ack = a if and only if limk ack,; - di for all it , .... ~ ]

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