METRIZABILITY OF ORDERED ADDITIVE GROUPS

被引：2

作者：

Liu, Chuan ^{[1
]}

Tanaka, Yoshio ^{[2
]}

机构：

[1] Ohio Univ, Dept Math, Zanesville Campus, Zanesville, OH 43701 USA

[2] Tokyo Gakugei Univ, Dept Math, Tokyo 1848501, Japan

来源：

TSUKUBA JOURNAL OF MATHEMATICS | 2011年 / 35卷 / 02期

关键词：

metrizability; linearly ordered topological space; order topology; ordered additive group; ordered field; Archimedes' axiom; axiom of continuity;

D O I：

10.21099/tkbjm/1331658702

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In terms of General Topology, we consider ordered additive groups having the order topology, including ordered fields. Namely, we investigate metrizability of these groups or fields, and topological properties of ordered fields in terms of Archimedes' axiom or the axiom of continuity. Also, we give a negative answer to a question in [9]. Finally, we revise the proof of [2, Theorem 2.6], and give some related results.

引用

页码：169 / 183

页数：15

共 11 条

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