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Homework Help: If the inverse of a function maps base sets to base sets, then the fn is continuous?

  1. Dec 5, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove that if the inverse of a function between topological spaces maps base sets to base sets, then the function is continuous.


    2. Relevant equations
    I have no idea.


    3. The attempt at a solution
    I seriously have no idea. This is for my analysis course, and I'm not sure why the prof is going over topology. I have some PDF's so I have some idea about open sets and continuous functions but not enough to solve this proof.
     
  2. jcsd
  3. Dec 5, 2012 #2
    Re: If the inverse of a function maps base sets to base sets, then the fn is continuo

    Maybe start by giving the definition of a continuous function? What is it that you need to prove?

    Also start by defining basis.
     
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