Choban operators in generalized ordered spaces
type: Item
instance of: scholarly article
title: Choban operators in generalized ordered spaces
zbMATH Open document ID: 1261.54018
published in: Topology and its Applications
publication date: 2013-03-15T00:00:00Z
review text: A Choban operator on a topological space \(X\) is a continuous map from~\(X^2\) to~\(X\) that is constant on the diagonal and that maps each vertical line \(\{x\}\times X\) bijectively onto~\(X\). A topological group has an obvious Choban operator: the map \(\langle a,b\rangle\mapsto ab^{-1}\). The authors investigate this and related notions in the class of GO-spaces. They show that a GO-space with a Choban operator is hereditarily paracompact, that first-countable LOTS with a Choban operator are metrizable and that the real line is the only non-trivial connected LOTS with a Choban operator. Among the delimiting examples are: an ultrapower of the real line as a non-metrizable LOTS that is a topological group; the Sorgenfrey and Michael lines have Choban operators; there are Bernstein subsets of the real line with and without Choban operators; and only \textit{open} intervals of the real line have Choban operators.
reviewed by: K. P. Hart
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54B05
Mathematics Subject Classification ID: 54H11
zbMATH DE Number: 6145455
zbMATH Keywords: Choban space
zbMATH Keywords: flexible diagonal
zbMATH Keywords: rotoid
zbMATH Keywords: continuously homogeneous space
zbMATH Keywords: Bernstein set
zbMATH Keywords: Sorgenfrey line
zbMATH Keywords: Michael line
zbMATH Keywords: GO-space
zbMATH Keywords: LOTS
author: Harold Bennett
author: Dennis Burke
author: David Lutzer
MaRDI profile type: Publication
full work available at URL: j.topol.2013.01.009
OpenAlex ID: W2058399980
DOI: 10.1016/J.TOPOL.2013.01.009
description: scientific article; zbMATH DE number 6145455