| Title:
|
Topology on ordered fields (English) |
| Author:
|
Tanaka, Yoshio |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
139-147 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $F$. (English) |
| Keyword:
|
order topology |
| Keyword:
|
subspace topology |
| Keyword:
|
ordered field |
| Keyword:
|
Archimedes' axiom |
| Keyword:
|
axiom of continuity |
| MSC:
|
12J15 |
| MSC:
|
54A10 |
| MSC:
|
54F05 |
| idZBL:
|
Zbl 1249.54072 |
| idMR:
|
MR2880916 |
| . |
| Date available:
|
2012-02-07T10:29:10Z |
| Last updated:
|
2014-04-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141831 |
| . |
| Reference:
|
[1] Engelking R.: General Topology.Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[2] Gillman L., Jerison M.: Rings of continuous functions.D. Van Nostrand Co., Princeton, N.J.-Toronto-London-New York, 1960. Zbl 0327.46040, MR 0116199 |
| Reference:
|
[3] Liu C., Tanaka Y.: Metrizability of ordered additive groups.Tsukuba J. Math. 35 (2011), 169–183. |
| Reference:
|
[4] Tanaka Y.: The axiom of continuity, and monotone functions.Bull. Tokyo Gakugei Univ. Nat. Sci. 57 (2005), 7–23, (Japanese). Zbl 1087.26500, MR 2286673 |
| Reference:
|
[5] Tanaka Y.: Ordered fields and metrizability.Bull. Tokyo Gakugei Univ. Nat. Sci. 61(2009), 1-9. Zbl 1185.54035, MR 2574357 |
| Reference:
|
[6] Tanaka Y.: Ordered fields and the axiom of continuity. II.Bull. Tokyo Gakugei Univ. Nat. Sci. 63 (2011), 1–11. MR 1303666 |
| . |
