real analysis connected sets

**CarmineCortez** · November 1st 2008, 11:04 AM

Show that it is not necessarily true that if two connected sets have a non-empty intersection, then their intersection will be connected. (a picture will do)

not sure what this would be... any ideas?

**Plato** · November 1st 2008, 11:32 AM

$\begin{gathered}<br /> A = \left\{ {\left( {x,y} \right) \in \mathbb{R}^2 :y = \sqrt {1 - x^2 } ,-1 \leqslant x \leqslant 1} \right\} \hfill \\<br /> B = \left\{ {\left( {x,y} \right) \in \mathbb{R}^2 :y = - \sqrt {1 - x^2 } ,-1 \leqslant x \leqslant 1} \right\} \hfill \\ <br /> \end{gathered}$

**CarmineCortez** · November 1st 2008, 11:37 AM

what does it mean that the intersection is connected?

**Plato** · November 1st 2008, 12:06 PM

Originally Posted by CarmineCortez

what does it mean that the intersection is connected?

What is the intersection of those two arcs?

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