Connectedness of set which is an intersection of some connected set 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.
Try to intersect two bananas.$ $
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