Thread: help me solve this problem please..

f: R to R. For all open subset U of R, we have f(U) is open, too.


Prove that: f is monotonic.

Originally Posted by felixmcgrady

f: R to R. For all open subset U of R, we have f(U) is open, too.


Prove that: f is monotonic.

If $\displaystyle f$ is not monotonic, it will have a local extremum at some point $\displaystyle x_0$. What can you say about an open ball around $\displaystyle f(x_0)$?