Planar-topologische Fastkörper

Topological planar nearfields (F, T) are suitable for coordinatizing topological affine and projective planes only if the solutions of equations of the type ax - bx = c, a ≠ b, depend continuously on a, b, c ∈ F. In this case we call T a p-topology and deal with the problem, under which conditions a nearfield topology even is a p-topology. Satisfactory answers are given in each of the following three situations: 1. T is induced by a valuation. 2. T is locally compact. 3. F is derived from a coupling κ on a topological skewfield with an open kernel and with continuous images κ (a). Furthermore, it is shown that the interval topology of an ordered nearfield always is a p-topology.