So, I know P. Enflo showed that there is a separable Banach Space that doesn't satisfy the approximation property. My professor mentioned during class that in fact generic separable Banach Spaces don't have a Schauder basis where generic is in terms of Baire Category with some topology. I was hoping someone could outline how we put a topology on the space of all Banach Spaces in order to show dense $G_{\delta}$.
Also, an outline of how we show density since I assume we end up showing comeagerness of our set.