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What's the questions asking me to show?

  1. Jan 20, 2010 #1
    What is a question in topology asking of me when it says show that the topology of S1 and a quotient space agree?
     
  2. jcsd
  3. Jan 20, 2010 #2
    That the topologies are equal. A topological space is a set X with a topology T. In your case you are probably given a set S1 with a topology T1 (maybe product topology, maybe subspace topology, maybe discrete topology, maybe some other topology) and you are given a quotient map [itex]q : Y \to S1[/itex] where Y is a topological space and this induces the quotient topology T2 on S1. You are now asked to show that a set is open in (S1,T1) if and only if it is open in (S1,T2).
     
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