I've to prove that the set of all subjective bounded linear operator is a closed subset of B(X, Y).
I tried with a sequence $T_n$ of surjective bounded maps, suppose it converges to some T $\in$ B(X, Y).
I've to show now T is surjective and bounded.
Let y $\in$ Y, for each $T_n$ there exists $x_n \in$ X such that $T_n(x_n)=y$.
Can someone help me how to proceed from here?