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Math Help - real analysis connected sets

  1. #1
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    real analysis connected sets

    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?
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  2. #2
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    \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}
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  3. #3
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    what does it mean that the intersection is connected?
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  4. #4
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    Quote Originally Posted by CarmineCortez View Post
    what does it mean that the intersection is connected?
    What is the intersection of those two arcs?
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