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Quotient topology

  1. Apr 15, 2013 #1
    Hi,
    I am trying to prove the following proposition:
    Let F be a closed subset of the Euclidean space Rn.Then the quotient space Rn/F is first countable if and only if the boundary of F is bounded in Rn.
    Any ideas?
     
  2. jcsd
  3. Apr 15, 2013 #2

    tiny-tim

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    Homework Helper

    hi hedipaldi! :smile:
    "if and only if", so that's two proofs …

    which one can you do?​

    (start by setting out the definitions)
     
  4. Apr 15, 2013 #3
    you say that one side follows directly from the definitions?I am not so experienced in dealing with quotient spaces (though i am familiar with the definitions) so i really need some hints.
     
  5. Apr 15, 2013 #4

    tiny-tim

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    no, i'm saying that you haven't shown any work, you haven't used the homework template, and writing out the definitions would be a good way to start

    try now ​
     
  6. Apr 15, 2013 #5
    The definitions are not the problem,i have them in front of me. I just need some hints (I am not a student and this is not homework,i am only curious to solve it)
     
  7. Apr 15, 2013 #6

    Mark44

    Staff: Mentor

    tiny-tim has given you a hint - start writing some definitions, such as those for a first countable space and the boundary of a set.
     
  8. Apr 15, 2013 #7

    Mark44

    Staff: Mentor

    I am moving this thread to Homework & Coursework section.

    From the PF Rules:
     
  9. Apr 15, 2013 #8

    Mark44

    Staff: Mentor

    Moved material from a separate but related thread into this one.
     
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