I'm facing some troubles with the following theorem,
Let $X,Y$ be Banach spaces and let $T \in B(X,Y)$. I want to show that if $T$ is bijective then its inverse is continuous. Now if $T$ is bijective than its surjectivity implies that it is open by the open mapping theorem. From here on I need do deduce that $T^{-1}$ is continuous but I don't see it really.
Can someone help me with this?
thanks in advance