Topological geometry

One may topologise an incidence structure by imposing that the operations of joining points and intersecting lines are continuous. This project investigates two different approaches to this. We first show that with respect to the canonical topology of the real affine and projective planes, these operations are continuous. Then, without a canonical topology at hand, we construct a topology on the line set of the Moulton planes so that these operations are continuous. Furthermore, we show that this topology is essentially unique