Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 35 (1994), No. 2, 181-191.

Criteria for Two-Dimensional Circle Planes

Burkard Polster, G\"unter F. Steinke

Abstract.

We give some easy to use criteria for deciding whether a
M\"obius plane, Laguerre plane or Minkowski plane, given in some
normal form, is 2-dimensional. As an application of our results we
prove that a Laguerre plane or Minkowski plane with a given topology 
on the point set is a (topological) 2-dimen\-sional plane if and only 
if each derived affine plane at points of at least one parallel class 
is 2-dimensional with respect to the induced topology.