ALGEBRAIC ORDER TOPOLOGIES, AND RELATED MATTERS

Yoshio Tanaka; Yoshimi Kitamura

doi:10.21099/tkbjm/20234702191

Abstract

The order topologies on ordered sets are well-known. For ordered groups or ordered rings, we investigate algebraic order topologies which are compatible with their operations. We consider these topologies on the products of ordered groups, the product extension rings of ordered rings, and also Archimedean ordered groups. We give examples related to algebraic order topologies, etc.

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Yoshio Tanaka. Yoshimi Kitamura. "ALGEBRAIC ORDER TOPOLOGIES, AND RELATED MATTERS." Tsukuba J. Math. 47 (2) 191 - 206, December 2023. https://doi.org/10.21099/tkbjm/20234702191

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Received: 11 January 2023; Revised: 15 June 2023; Published: December 2023

First available in Project Euclid: 18 March 2024

Digital Object Identifier: 10.21099/tkbjm/20234702191

Subjects:

Primary: 06F20 , 12J15 , 13J25 , 54B05 , 54F05

Keywords: algebraic order topology , Archimedean ordered group , cone , metrizable space , order topology , ordered group , ordered ring , product extension ring , subspace topology , Topological Group

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