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This question is about "Real Analysis".


Start with a set S c R and successively take its closure, the complement of its closure, the closure of that, and so on: S, cl(S), (cl(S))c,.... Do the same to Se. In total, how many distinct subsets of R can be produced this way? In particular decide whether each chain S, cl(S), consists of only finitely many sets. For example, if S = Q then we get Q, R, , , R, R, and Qe, R, 0, 0, R, R,.. for a total of four sets.

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Answer #1

L eh kS → closure S. Fir사 Ckikis-Ks 2 a~. , this h.pes thate. 14 is lem

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