Bitopologies on totally ordered sets
type: Item
instance of: scholarly article
title: Bitopologies on totally ordered sets
zbMATH Open document ID: 0932.54032
DOI: 10.1023/A:1006615322722
author: Ralph Kopperman
author: Richard G. Wilson
published in: Acta Mathematica Hungarica
publication date: 2000-02-21T00:00:00Z
review text: The authors study the category of so-called ray bispaces, that is, the category whose objects are totally ordered sets with two topologies, each having a subbase of rays and so that the resulting bitopological space is pairwise weakly symmetric, and whose morphisms are the pairwise continuous functions. Among other things, they show that such spaces are (pairwise) monotonically normal, obtain a bitopological version of the Intermediate Value Theorem and give conditions for the equality of the de Groot dual and the ray dual of a ray topology. They also show that a selective ray topology is compact if and only if it is skew compact.
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 1404416
zbMATH Keywords: ray bispace
zbMATH Keywords: ray topology
zbMATH Keywords: pairwise monotonically normal
zbMATH Keywords: pairwise connected
zbMATH Keywords: de Groot dual
zbMATH Keywords: ray dual
zbMATH Keywords: category
zbMATH Keywords: bitopological space
zbMATH Keywords: pairwise continuous functions
reviewed by: Hans Peter Künzi
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1404416