Question: Problem 4. Let X be a set. Consider two metrics di and d2 on X. Let(Ti and T2 be the metric topology generated by dj

Problem 4. Let X be a set. Consider two metrics di and d2 on X. Let(Ti and T2 be the metric topology generated by dj and d2 respectively. In other words, T, is the set of all unions of open balls in (X, d;) for i = 1, 2. 1. Suppose that for each r ( X and r > 0, there exists an s > 0 such that Ba, (I, s) C Baz (x, r). What is the relationship between 71 and T2? 2. Suppose that for each r ( X and r > 0, there exist s1 > 0 and $2 > 0 such that Ba, (1, 51) C Bda (x, r) and Bda (X, $2) C Bad, (x, r). What is the relationship between 7, and Tz

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