Talk:Cover of Interval By Closed Intervals is not Pairwise Disjoint

While attending to the tidying of this page (trying to fix the proof on-the-fly) it eventually occurred to me that we can simply take $\JJ = \set {\closedint x x: x \in I}$ as a perfectly fine cover. Thus probably the intervals need some condition leading to them having non-empty interior. Because there is no imposition on $\JJ$ the current purported proof will fail, because an interval like $\JJ$ may not exist. --Lord_Farin (talk) 21:53, 12 February 2013 (UTC)