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Title :Ordered fields and metrizability
Title alternative :順序体と距離化可能性
Authors :TANAKA,Yoshio
Authors alternative :田中,祥雄
Issue Date :30-Sep-2009
Abstract :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.
URL :http://ci.nii.ac.jp/books/openurl/query?url_ver=z39.88-2004&crx_ver=z39.88-2004&rft_id=info%3Ancid%2FAA12070144
Type Local :紀要論文
ISSN :18804330
Publisher :東京学芸大学学術情報委員会
URI :http://hdl.handle.net/2309/147808
Comment :論文
text version :publisher
Citation :東京学芸大学紀要. 自然科学系 Vol.61 p.1 -9
Appears in Collections: Bulletin of Tokyo Gakugei University. Natural Sciences(ISSN:18804330)

Please use this identifier to cite or link to this item: http://hdl.handle.net/2309/147808