This question already has an answer here:
- Open Mapping Theorem: counterexample 1 answer
The open maping theorem between banach spaces says.
Let $T:X\to Y$ be a linear,continuous and surjective map between the banach spaces $X,Y$ then $T$ is an open map.
I need examples to show that the completeness assumption are important even in the presence of completeness of the other space. Thanks!