Let $X,Y$ be Banach spaces. Prove a subspace in $B(X,Y)$ is open.

Question

Suppose $X$ and $Y$ are Banach spaces, Prove that $O=\{T \in B(X,Y):T^*(Y^*)=X^*\}$ is open in $B(X,Y)$. (note:$B(X，Y)$ is the set of all bounded linear operators from $X$ to $Y$ .) i have no idea how to prove open for a set of operators, should I consider open ball? I hope get proof of this question, thanks a lot.