On homeomorphisms and incidence relations of compact projective planes (Q1812978)

In general it is not known whether the point space of a topological projective plane is always homeomorphic to the line space. In this paper we present a general method of constructing a homeomorphism from the point space onto the line space of a compact projective plane. As first application, we show that the point space of a compact connected translation plane is always homeomorphic to the line space. Moreover, it follows that the incidence relations of many compact connected projective planes are noncontinuous in the sense of \textit{G. Grimeisen} [Acta Math. Hung. 41, 241-250 (1983; Zbl 0528.51002)].