I want to ask some thing about a counterexample for the open mapping theorem:
Find a discontinuous linear mapping $T: \ X \to Y$ such that $T(X)=Y$ and $X,Y$ are Banach but $T$ is not open.
I find there is a answer in the link below:
But I don't understand how to prove clearly three cases b), c) and d), especially the case c).
Anyone can help me?