- #1
ehrenfest
- 2,020
- 1
Homework Statement
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?