Please do problem6 thank you A map f X rightarrow Y of topol

A map f: X rightarrow Y of topological spaces is called an open map if for every open set U X, the image f(U) Y is also open. Prove or disprove: If f is open then it is continuous. If f is a homeomorphism then it is open. If f is an open, continuous bijection, it is a homeomorphism. If f: R rightarrow R is a continuous surjection, it is open. If f: R rightarrow R is a continuous open surjection, it is a homeomorphism.

Solution

If fuction is Real thatn it will always be homeomorphism.