Actually you are both WAAAAAAAAAAAAAY off.
True porn insiders like Darth & I spend most of our time expanding our knowledge of Point-Set Topology, in this case the nature of the
finite intersection property, (FIP).
We define specific subset collections of a mutually agreed upon chosen set and take turns attempting to ascertain if the intersection over any finite subcollection of the collection is nonempty, and thus, one could say, has FIP.
Simple.
Sierpinski space, anyone??