Considering the set X = {1,2,3,4,5,6,7,8}, calculate a Tx topology on X such that the...

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Considering the set X = {1,2,3,4,5,6,7,8}, calculate a Tx topology on X such that the following two conditions are met:Tx has exactly 8 different elements, that is, | Tx | = | X | = 8It is possible to find a subspace S of X with three elements, such that the relative topology Ts in S (with respect to Tx) has exactly 8 different elements, that is, | Ts | = | Tx | = | X | = 8Given f: X - >> S (function of X over S), compute the smallest topology Tf over X, such that f is in C (X, S) with respect to the topology Ts over S. Is it possible to compare Tf with Tx?Given g: S> -> X (one-to-one function of S in X), compute the smallest topology Tg over S, such that f is in C (S, X) with respect to the topology Tx over X. Is it possible to compare Tg with Ts?

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