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.
Connectedness of set which is an intersection of some connected set
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$\begingroup$
general-topology
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0intersection maybe? – 2012-12-05
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7Try to intersect two bananas. – 2012-12-05
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0Do you mean an intersection a collection of connected sets? Draw pictures in the plane. – 2012-12-05
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1@ArthurFischer The thing escaped me, but you are right, I definitely should have. :-) – 2012-12-05
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1@JasperLoy An excellent movie. – 2012-12-05
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1@did You should make your comment into an answer. – 2012-12-05
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1@MattN. Done. $ $ – 2012-12-06
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0At least contained in [this](http://math.stackexchange.com/q/55646/8271) – 2013-02-26
2 Answers
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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