These two theorems are equivalent but I can not figure out how to deduce the open mapping from the closed graph. Can anyone give a hint or some reference?
The proof linked to by David is the standard one, but the write-up strikes me as somewhat clumsy.
Here's my take on this argument:
Suppose $T: X \to Y$ is continuous and onto.
Note: Step 2. is a proof of the inverse mapping theorem from the closed graph theorem.