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Topology problem

  1. Oct 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Let U be a topology on the set Z of integers in which every infinite subset
    is open. Prove that U is the discrete topology, in which every subset is open.

    2. Relevant equations

    Just the definition of discrete topology

    3. The attempt at a solution

    I'm not sure where to start!
     
  2. jcsd
  3. Oct 9, 2009 #2
    yeah i think that this is the same method used in the other thread someone else made with the second part of this question. find two infinite subsets of Z that intersect at a single point. then by doing this for every element of Z you can show that every 1 element subset of Z is open. then u can take arbitrary unions to show every possible subset of Z is open and hence U is the power set of Z.
     
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