Show that if f: X->Y is a homeomorphism, then:
I am stuck!
Originally Posted by Andreamet Show that if f: X->Y is a homeomorphism, then: I assume A is a subset of X.
Since , .
We need to show that is , which is .
1. For every subset A of X, one has when f is continuous. If f is a homeomorphism, .
2. . Using 1, .
Now, it remains to combine 1 & 2 to get the answer.