Geometries on surfaces

Helmut R. Salzmann

Vol. 29 (1969), No. 2, 397–402

DOI: 10.2140/pjm.1969.29.397

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.

Mathematical Subject Classification

Primary: 57.05

Milestones

Received: 5 March 1968

Published: 1 May 1969