Helmut Salzmann

Projectivities and the Topology of Lines

A topological projective plane is a projective plane P = (P, L) such that P and L are topological spaces (neither discrete nor indiscrete) and join and intersection are continuous: for any open set U the set of all pairs of distinct lines intersecting in a point of U is open in L 2 and dually.

Elations in four-dimensional planes

Abstract Let K and L be two distinct lines of a topological projective plane which is homeomorphic to the complex plane. If for each center c ϵ K there exists a homology ≠1 with axis L , then the elation group with center K ∩ L and axis L is transitive.