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Thread: quotient map, open map

  1. #1
    Dec 2008

    quotient map, open map

    Let $\displaystyle \pi: \mathbb{R} \times \mathbb{R} \rightarrow \mathbb{R}$, $\displaystyle (x, y) \mapsto \pi(x, y)=x$.
    Let $\displaystyle A=(\mathbb{R}^{\geq 0} \times \mathbb{R}) \cup (\mathbb{R} \times \{0\})$.
    Prove that $\displaystyle f=\pi|_A$ is a quotient map and that $\displaystyle f$ is neither an open map or a closed map.

    [$\displaystyle \mathbb{R}^{\geq 0}=\{ x\in \mathbb{R}: x\geq 0\}$]
    [This is Munkres 22.3]
    Last edited by GenoaTopologist; Jan 16th 2009 at 04:07 AM.
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