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Thread: Prove a property of covering maps: p p′

  1. #1
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    Prove a property of covering maps: p p′

    I just read a property of covering maps:
    If p : EB and p′ : E′ → B′ are covering maps, then so is the map p p′ : E E′ → B B′ given by (p p′)(e, e′) = (p(e), p′(e′)).

    But how do I prove it?

    Since I'm new to this area, so I first thought of starting with the definition. But then given an open set U of B B′, I can't break it with regard to B and B'. What should I do?
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  2. #2
    Super Member Rebesques's Avatar
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    Re: Prove a property of covering maps: p p′

    Αn open set in $\displaystyle B\times B'$ will be of the form $\displaystyle U\times U'$, and so you can use the covering property component-wise:
    $\displaystyle (p\times p')^{-1}(U\times U')=(p^{-1}(U),p'^{-1}(U'))$.
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