Yoshio Tanaka
Topology on ordered fields

Comment.Math.Univ.Carolin. 53,1 (2012) 139-147.

Abstract:An ordered field is a field which has a linear order and the order topology by this order. For a subfield $F$ of an ordered field, we give characterizations for $F$ to be Dedekind-complete or Archimedean in terms of the order topology and the subspace topology on $F$.

Keywords: order topology, subspace topology, ordered field, Archimedes' axiom, axiom of continuity
AMS Subject Classification: 54A10 54F05 12J15