Q Let X be an Infinite sel with topdogy ?. Prove or disprove : (a) If every mfinite Suhsel of x i closed Xs clased In (X7), then is the discrete topoloy. (b) If every infinite Subset of X is open In (X.x), then is the diserete topology. Solution.

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A: given that (1) (a)                                    S=n(-1)n:n∈N=2k(-1)2k:n=2k,…

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Q: 11. If a set has empty interior, then so does its closure. 12. The closure of a set coincides with…

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A: a. Interior point is empty b. Boundary of set S is all point of set S c.  Set S is closed.

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Q: Let Y be an infinite subset of a compact set XC R. Prove Y' 0.

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Q: Theorem 7.42. The Cantor set is homeomorphic to the product InEN{0, 1} where {0, 1} has the discrete…

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