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Is a set which is an intersection of some connected set still connected? I think it is not true but could not think of an example.

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marked as duplicate by Erick Wong, Micah, Asaf Karagila, Stefan Hansen, Alexander Gruber Feb 26 '13 at 11:35

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Try to intersect two bananas. – Did Dec 5 '12 at 7:57
@did: I'm surprised you didn't suggest intersecting $\mathsf{M}$ and $\mathsf{W}$. – Arthur Fischer Dec 5 '12 at 7:58
@ArthurFischer The thing escaped me, but you are right, I definitely should have. :-) – Did Dec 5 '12 at 8:02
@JasperLoy An excellent movie. – Did Dec 5 '12 at 8:19
@did You should make your comment into an answer. – Rudy the Reindeer Dec 5 '12 at 10:09

2 Answers 2

up vote 5 down vote accepted

Try to intersect two bananas.$ $

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I think that is true. Take an example in $\mathbb{R}$, 3 intervals [0,1],[$\frac{1}{2}$,$\frac{3}{2}$],[$\frac{5}{4}$,2], their intersection is [$\frac{1}{2}$,1] and [$\frac{5}{4}$,$\frac{3}{2}$] is separated

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