Geometries on surfaces

Abstract

Among the topological geometries, two classes have so far attracted special attention, namely the locally compact, 2- dimensional projective and affine planes. Such a plane has a pointset which is homeomorphic to the pointset of the real arguesian plane, hence is a 2-dimensional manifold. In this paper, all the 2-manifolds that can carry topological geometries with connected lines will be determined. © 1969 by Pacific Journal of Mathematics.