The transposition of locally compact,connected translation planes

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