Tsukuba Journal of Mathematics

Metrizability of ordered additive groups

Chuan Liu and Yoshio Tanaka

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Abstract

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.

Article information

Source
Tsukuba J. Math., Volume 35, Number 2 (2011), 169-183.

Dates
First available in Project Euclid: 13 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1331658702

Digital Object Identifier
doi:10.21099/tkbjm/1331658702

Mathematical Reviews number (MathSciNet)
MR2918315

Zentralblatt MATH identifier
1244.54069

Subjects
Primary: 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces [See also 06B30, 06F30] 54H11: Topological groups [See also 22A05] 54E35: Metric spaces, metrizability

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

Citation

Liu, Chuan; Tanaka, Yoshio. Metrizability of ordered additive groups. Tsukuba J. Math. 35 (2011), no. 2, 169--183. doi:10.21099/tkbjm/1331658702. https://projecteuclid.org/euclid.tkbjm/1331658702


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