Yeah, I should have made more clear, I am aware of that, basically what I was trying to say is I think your paradigm might be inconsistent with what the book is trying to do (not that what the book is trying to do necessarily makes sense). Anyway like I said earlier it is an interesting paradigm, I’d actually never seen it before. By the way regarding the “continuous family of topological spaces” (by which I guess you mean the map sending a point to its fiber under a continuous map), is there a topology on the space of topological spaces such that the family is actually continuous?
Yeah, I should have made more clear, I am aware of that, basically what I was trying to say is I think your paradigm might be inconsistent with what the book is trying to do (not that what the book is trying to do necessarily makes sense). Anyway like I said earlier it is an interesting paradigm, I’d actually never seen it before. By the way regarding the “continuous family of topological spaces” (by which I guess you mean the map sending a point to its fiber under a continuous map), is there a topology on the space of topological spaces such that the family is actually continuous?