- #1
rhino1000
- 34
- 1
I don't see how this is the case. Let ao and bo be members of [A,B] with ao<bo. Let {ai} be a strictly decreasing sequence, with each ai>A and {bi} be a strictly increasing sequencing with each bi<B. Let the limits of the two sequences be A and B, respectively. Then define Ii = [ai,bi]. It seems to me that the union of {Ii} is an open set, not a closed set. Thoughts?