Geodesic
Topology on ordered fields
Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 1, pp. 139-147.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 $F$.
Classification : 12J15, 54A10, 54F05
Keywords: order topology; subspace topology; ordered field; Archimedes' axiom; axiom of continuity 
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Tanaka, Yoshio. Topology on ordered fields. Commentationes Mathematicae Universitatis Carolinae, Tome 53 (2012) no. 1, pp. 139-147. http://geodesic.mathdoc.fr/item/CMUC_2012__53_1_a9/