Is the intersection of two connected set is connected?? I think it is connected, I can't find any counter example to prove it disconnected. My approach is-> A,B connected. Let A meet B disconnected,A meet B =PUQ where P,Q are separated set What next??
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Intersect an annulus centred at zero with a line through the origin – FShrike Jun 27 '23 at 14:41
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1Choose $A=\Bbb{S}^1$ and $B=\textrm{X -axis}$ in $\Bbb{R}^2$.Then $A\cap B={(-1, 0), (1, 0) }$ – SoG Jun 27 '23 at 14:46
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@GEdgar no, As I know the empty set is trivially connected. So it must not be a counter example – Arghya Santra Jun 27 '23 at 15:53
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1You are missing the point of that answer. – Randall Jun 27 '23 at 16:08
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I think this is a better Counter example
Arghya Santra
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1This question goes against our quality standard policy. Instead of posting an answer, you should encourage the person who posted the question to improve it. – José Carlos Santos Jun 29 '23 at 13:32