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Question: st eduuymordeckicoursesmedida2013bookpdf 12 theorem 13 states that every open set...

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st edu.uy/-mordecki/courses/medida2013/book.pdf 12. Theorem 1.3 states that every open set in R is the disjoint union of open intervals. The analogue in R, d2 2, is generally false. Prove the following (a) An open disc in R? is not the disjoint union of open rectangles Hint: What happens to the boundary of any of these rectangles?] An open connected set Ω is the dis oint union of open rectangles if and only if Ω is itself an open rectangle.

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