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Math Help - Open - Close Function.

  1. #1
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    Open - Close Function.

    Hello, Im trying to prove the following function is open but not close. I really have no idea how to do it. I just know the concept but nothing else. Please help.



    $\pi _1 :\mathbb{R}^2  \to \mathbb{R} \hfill \\$
     $\pi _1 \left( {x_1 ,x_2 } \right) = x_1  \hfill \\ $
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  2. #2
    Super Member girdav's Avatar
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    Take E:=\left\{\left(x,\frac 1x\right),x>0\right\}. This is a closed subset of \mathbb{R}^2. What is \pi_1(E) ?
    Take U an open subset of \mathbb R^2 and x\in \pi(U). Let  (x,y') such that \pi (x,y)\in U. We can find I_1 and I_2 two open intervals such that (x,y)\in I_1\times I_2 \subset U.
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