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Restriction of a function

  1. Dec 6, 2007 #1
    1. The problem statement, all variables and given/known data
    This is a topology.

    Let f: X -> Y be a bijective function.

    If I want to show that [tex] f|_{A}[/tex], where A is a set in X, is a homeomorphism, I need to show that:

    1)If U is open in the subspace topology of f(A) (w.r.t. Y), then f^{-1}(U) is open in the subspace topology on A (w.r.t X)

    2)If U is open in the subspace topology of A (w.r.t X), then f(U) is open in the subspace topology on f(A) (w.r.t. Y)

    and then I am done, correct?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 6, 2007 #2

    morphism

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    Yes. That will prove that f|A is a homeomorphism between A and f(A).
     
  4. Dec 6, 2007 #3
    Thanks. That helps!
     
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