Question 2: A set S is said to be totally bounded if for all e > 0 there exists finitely many points 81, ..., Sn ES such

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Question 2 A Set S Is Said To Be Totally Bounded If For All E 0 There Exists Finitely Many Points 81 Sn Es Such 1 (54.99 KiB) Viewed 18 times

Question 2: A set S is said to be totally bounded if for all e > 0 there exists finitely many points 81, ..., Sn ES such that n scÜ(s; – €, 8; +€). j=1 Prove that a subset SCR is totally bounded if and only if it is bounded. In the next two questions we consider the important concept of relative topology. For a set X and a topology T on X, given a subset S CX we induce a new topology Ts on S from T by putting Ts = {SNU:U ET}. In other words the topology TS consists of intersections of S with open sets in T. A subset ACS is said to be relatively open in S if and only if there exists an open set U ET such that A= Snu.