Hey guys, doin another rudin-related question. Here Goes: 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(an,bn). (It's possible that an=-[tex]\infty[/tex] bn=+[tex]\infty[/tex] for some n.) My attempt: Take the set of all Neighborhoods of all of the rationals of a rational radius in R to be A. 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?