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Thread: quotient map, open map

  1. #1
    Dec 2008

    quotient map, open map

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

    [ \mathbb{R}^{\geq 0}=\{ x\in \mathbb{R}: x\geq 0\}]
    [This is Munkres 22.3]
    Last edited by GenoaTopologist; Jan 16th 2009 at 05:07 AM.
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