Prove that the complement of a dense open subset of R is nowhere dense in R

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A: By properties of Measurable set,         If then  .

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A: Please check the answer in next step

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Q: Let F= {Fa: a € A} be a family of compact subsets of R. Prove a€A Fa is compact.

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A: A can be written in interval form

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Q: Use the definition of compactness to prove that a closed subset Y of a compact set XCR is compact.

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Q: 39. Let (J,≤) be the partially ordered set with J = {0,1} and with 0 < 1. By identifying the subsets…

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