Topological affine spaces (Q1262530)

\textit{K. Sörensen} [Beitr. Geom. Algebra, Proc Symp. Duisburg 1976, 305- 310 (1977; Zbl 0381.51008)] defined a topological affine space using topologies for the set of points and for the set of hyperplanes such that the joining of n independent points, the intersection of n independent hyperplanes and the constructions of parallel hyperplanes are continuous operations. Now a characterization of such spaces is given by means of the topologies on the sets of points and lines using the continuity of the following geometric operations (when defined): A1) joining of two points, A2) interseting two lines, A3) drawing the parallel line, A4) intersecting lines with a given hyperplane. For dimension two both notions coincide.