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(a,b) not homeomorphic to [a,b]

  1. Nov 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Show that (0,1) is no homeomorphic to [0,1]


    2. Relevant equations



    3. The attempt at a solution

    I understand the usual procedure for proving this - remove a point from each of the spaces and check for connectedness. My only question is, the topology on each space isn't specified. Do I assume it's the subspace topology or what?

    In general, when given questions like this, with no topology given, do I just infer from the context of the question which topology I should use?
     
  2. jcsd
  3. Nov 9, 2011 #2
    Nevermind guys. Looks like I need to pay more attention. My book says to assume the standard topology unless otherwise noted.
     
  4. Nov 9, 2011 #3

    Office_Shredder

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    This is a pretty awesome way of proving they're not homeomorphic to be honest. I think most people would just show that one is compact and the other is not
     
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