Thread: prove or disprove

there exists f: R-R, continuous, but not one to one, such that f(V) is open for any open subset V of R.

Any ideas will be appreciated, thanks!

Originally Posted by violetsf

there exists f: R-R, continuous, but not one to one, such that f(V) is open for any open subset V of R.

Any ideas will be appreciated, thanks!

f(x) = x^2

it is not R-R

Originally Posted by violetsf

it is not R-R

So you want an onto map also?

yes

Originally Posted by ThePerfectHacker

So you want an onto map also?