Document Type

Article

Department

Mathematics (HMC)

Publication Date

9-1-1987

Abstract

The topology most often used on a totally ordered group (G, <) is the interval topology. There are usually many ways to totally order G x G (e.g., the lexicographic order) but the interval topology induced by such a total order is rarely used since the product topology has obvious advantages. Let ℝ(+) denote the real line with its usual order and Q(+) the subgroup of rational numbers. There is an order on Q x Q whose associated interval topology is the product topology, but no such order on ℝ x ℝ can be found. In this paper we characterize those pairs G, H of totally ordered groups such that there is a total order on G x H for which the interval topology is the product topology.

Comments

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,278.

Publisher pdf, posted with permission. ISSN: 0305-0041

Article can also be found at http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2103000&fulltextType=RA&fileId=S030500410006730X

Rights Information

© 1987 Cambridge Philosophical Society

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Download

Included in

Mathematics Commons

Share

COinS