Proposition 4.4.6. A subset A of a metric space S is closed if and only if A' C A. When we considered the set A = (0,1) in R, we observed that A' = [0, 1). Clearly A' is not contained in A, thus by Proposition 4.4.6, A = (0, 1) is not closed. For a, b €R with a

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A:

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A:

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