Restriction of a function

1. Dec 6, 2007

ehrenfest

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 $$f|_{A}$$, 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. Dec 6, 2007

morphism

Yes. That will prove that f|A is a homeomorphism between A and f(A).

3. Dec 6, 2007

ehrenfest

Thanks. That helps!