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Math Help - Covering Map Question

  1. #1
    MHF Contributor Drexel28's Avatar
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    Covering Map Question

    In the definition of covering map is one to take the "disjoint union" of open sets \left\{O_j\right\}_{j\in\mathcal{J}} to literally be \coprod_{j\in\mathcal{J}}O_j=\bigcup_{j\in\mathcal  {J}}O_j\times\{j\} or is one to assume that the class of open sets is merely pairwise disjoint?
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  2. #2
    Senior Member Tinyboss's Avatar
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    It's the latter. The point is that each x has a neighborhood U whose inverse image consists of homeomorphic "copies" of U in the covering space.
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Tinyboss View Post
    It's the latter. The point is that each x has a neighborhood U whose inverse image consists of homeomorphic "copies" of U in the covering space.
    Yeah, homeomorphic copies who are disjoint. That makes much more sense, because then you'd have to define a whole new topology on this disjoint union, etc. Thanks!
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