著者

TANAKA Yoshio タナカ ヨシオ 田中 祥雄 田中 祥雄(東京学芸大学数学分野)

出版者

東京学芸大学学術情報委員会

雑誌

東京学芸大学紀要. 自然科学系 (ISSN:18804330)

巻号頁・発行日

vol.61, pp.1-9, 2009-09-30

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We recall that an ordered field is a field which has a linear order and the order topology (by this order). Order fields have played important roles in the theory of the real number field R in terms of Archimedes axiom or the axiom of continuity. Ordered fields give algebraic and topological principles in Analysis, Algebra, etc. with respect to the structure of the field R. In this paper, we give metrization theorems on ordered fields, and examples on non-Archimedean ordered fields, etc. Also, as materials around ordered fields, we consider metrizability of ordered (additive) groups, and definitions of real number fields.