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SOLVED: 1. (a) Prove that the set of prime numbers is a countable set.(b) Prove that in a usual metric space (R, d) each open ball is an open interval.(c) Prove that every finite set in a metric space is compact.(d) Do A and A have the same interior? Do A and A' have the same closure?(e) Prove that subsets of separated sets are separated.(f) Evaluate f(x) = 2a[x] x.(g) Prove that constant functions are uniformly continuous.(h) Prove that every upper Riemann integral is every upper Lebesgue int
SOLVED: 1. (a) Prove that the set of prime numbers is a countable set.…
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