Planar-topologische Fastkörper

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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.

Original languageEnglish
Pages (from-to)185-199
Number of pages15
JournalJournal of Geometry
Issue number1-2
StatePublished - 2002


  • Near-field
  • Topology


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