Arjana Žitnik: Quasi-topological configurations

Povzetek. It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not admit even realizations with pseudoline arrangements, i.e. they are not topological. We define the concept of a quasiline arrangement by relaxing the condition that two pseudolines meet exactly once and show that every combinatorial configuration can be realized as a quasiline arrangement in the real projective plane.

A quasiline arrangement with selected vertices belonging to the configuration can be viewed as a map on a closed surface. Such a map can be used to distinguish between two ``distinct" realizations of a combinatorial configuration as a quasiline arrangement.