The classification of compact punctally cohesive Desarguesian projective Klingenberg planes

It is shown that for a compact Desarguesian projective Klingenberg plane P with incidence structure P=#x2119;, , I and neighbour relation , where two distinct points always lie on some line, exactly one of the following holds: P is a non-discrete connected or totally disconnected ordinary projective plane with =id, P is a finite projective plane with =id, P is a finite projective Hjelmslev plane with id, or P is a non-discrete totally disconnected ordinary projective plane with id.Dedicated to H. Salzmann on his 60th birthdayThe author wishes to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) for their financial assistance in the writing of this paper.