The transposition of locally compact, connected translation planes

Abstract

This note deals with the transposition of translation planes in the topological context. We show that a topological congruence C of the real vector space R 2n has the property that every hyperplane of R 2n contains a component of C. This makes it possible to define the transposeP tau of the topological translation planeP associated with C; it is proved that the translation plane P τ is topological also. The relationship between collineation groups and the relationship between coordinatizing quasifields of P and P τ are also discussed.