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Keywords:
order topology; subspace topology; ordered field; Archimedes' axiom; axiom of continuity
order topology; subspace topology; ordered field; Archimedes' axiom; axiom of continuity
Summary:
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 $F$.
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