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