Hey guys, doin another rudin-related question. Here Goes:(adsbygoogle = window.adsbygoogle || []).push({});

Show that if E [tex]\subseteq[/tex] [tex]\Re[/tex] is open, then E can be written as an at most countable union of disjoint open intervals, i.e., E=[tex]\bigcup[/tex]_{n}(a_{n},b_{n}). (It's possible that a_{n}=-[tex]\infty[/tex] b_{n}=+[tex]\infty[/tex] for some n.)

My attempt:

Take the set of all Neighborhoods of all of the rationals of a rational radius inRto beA. Now all members of E intersect A make up E. Take the union of all of the neighborhoods in this set E intersect A and this is a countable union of disjoint sets.

Is there a problem with this?

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# Real analysis

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