Zur Fortsetzbarkeit von Ordnungsfunktionen einer affinen Ebene. (Extension of order functions of affine planes) (Q1079805)

An order function of a plane associates a number 1 or -1 with every triple consisting of a line and a pair of points not on the line, and is required to satisfy two conditions. Such an order function is an extension of the idea of two points lying on the same side or on opposite sides of a line. Let \(\Delta_ y\) denote the group of dilatations of an affine plane with centre y. The author shows that if for a point y of an affine translation plane \(| \Delta_ y| \geq 3\), then every order function of the plane can be extended to the projective closure.