Topology on ordered fields

Yoshio Tanaka

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 1, page 139-147
  • ISSN: 0010-2628

Abstract

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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 .

How to cite

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Tanaka, Yoshio. "Topology on ordered fields." Commentationes Mathematicae Universitatis Carolinae 53.1 (2012): 139-147. <http://eudml.org/doc/246444>.

@article{Tanaka2012,
abstract = {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 $F$.},
author = {Tanaka, Yoshio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {order topology; subspace topology; ordered field; Archimedes' axiom; axiom of continuity; order topology; subspace topology; ordered field; Archimedes' axiom; axiom of continuity},
language = {eng},
number = {1},
pages = {139-147},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Topology on ordered fields},
url = {http://eudml.org/doc/246444},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Tanaka, Yoshio
TI - Topology on ordered fields
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 1
SP - 139
EP - 147
AB - 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 $F$.
LA - eng
KW - order topology; subspace topology; ordered field; Archimedes' axiom; axiom of continuity; order topology; subspace topology; ordered field; Archimedes' axiom; axiom of continuity
UR - http://eudml.org/doc/246444
ER -

References

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  1. Engelking R., General Topology, Heldermann, Berlin, 1989. Zbl0684.54001MR1039321
  2. Gillman L., Jerison M., Rings of continuous functions, D. Van Nostrand Co., Princeton, N.J.-Toronto-London-New York, 1960. Zbl0327.46040MR0116199
  3. Liu C., Tanaka Y., Metrizability of ordered additive groups, Tsukuba J. Math. 35 (2011), 169–183. 
  4. Tanaka Y., The axiom of continuity, and monotone functions, Bull. Tokyo Gakugei Univ. Nat. Sci. 57 (2005), 7–23, (Japanese). Zbl1087.26500MR2286673
  5. Tanaka Y., Ordered fields and metrizability, Bull. Tokyo Gakugei Univ. Nat. Sci. 61(2009), 1-9. Zbl1185.54035MR2574357
  6. Tanaka Y., Ordered fields and the axiom of continuity. II, Bull. Tokyo Gakugei Univ. Nat. Sci. 63 (2011), 1–11. MR1303666

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