Topology on ordered fields

Commentationes mathematicae Universitatis Carolinae

Yoshio Tanaka¹ 

关键词: order topology;    subspace topology;    ordered field;    Archimedes' axiom;    axiom of continuity;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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 $F$.

【 授权许可】

CC BY