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Homework Help: Prove that a retraction is a quotient map

  1. Oct 30, 2012 #1
    1. The problem statement, all variables and given/known data

    As in title.

    2. Relevant equations

    Described in my attempt.

    3. The attempt at a solution

    screen-capture-29.png




    Where do I go from here? I need to show that those 2 unioned sets are open in A. I'm not seeing it
     
  2. jcsd
  3. Oct 30, 2012 #2
    Wait .... hang on .... I think I might have it.

    I know that (r^(-1) (U) ⋂ A) is open in A if we mean with respect to the subspace topology, since it is the intersection of an open set r^(-1) (U) of X with A. Not sure about the other unioned set though. Thoughts?
     
    Last edited: Oct 30, 2012
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