Question

REAL ANALYSIS Question 1 (1.1) Let A be a subset of R which is bounded above. Show that Sup A E A. (1.2) Let S be a subset of a metric space X. Prove that a subset T of S is closed in S if and only if T = SA K for some K which is closed in K. (1.3) Let A and B be two subsets of a metric space X. Recall that A°, the interior of A, is the set of interior points of A. (a) Prove that AºU B° C (AU B)º. (b) Give an example of two subsets A and B of the real line such that A'UB° + (AUB).

Answer 1

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