Abstract.
Topological planar nearfields (F,T) are suitable for coordinatizing topological affine and projective planes only if the solutions of equations of the type\( ax - bx = c, a \neq b \), depend continuously on\( a, b, c \in F \). 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. T is derived from a coupling \( \kappa \) on a topological skewfield with an open kernel and with continuous images \( \kappa(a) \).¶¶Furthermore, it is shown that the interval topology of an ordered nearfield always is a p‐topology.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 25 February 2001.
Rights and permissions
About this article
Cite this article
Wähling, H. Planar-topologische Fastkörper. J.Geom. 75, 185–199 (2002). https://doi.org/10.1007/s00022-002-1399-7
Issue Date:
DOI: https://doi.org/10.1007/s00022-002-1399-7