Coincidence of the Isbell and fine Isbell topologies
type: Item
instance of: scholarly article
title: Coincidence of the Isbell and fine Isbell topologies
zbMATH Open document ID: 1203.54011
author: Francis Jordan
published in: Topology and its Applications
publication date: 2010-09-24T00:00:00Z
review text: Let \(X\), \(Y\) be topological spaces and \(C(X,Y)\) denote the space of all continuous mappings from \(X\) into \(Y\). The author studies the relation between various topologies on \(C(X,Y)\) and when they coincide. The results rely on earlier work by \textit{S. Dolecki} and \textit{F. Mynard} [Topology Appl. 157, No. 8, 1370--1378 (2010; Zbl 1195.54036)]. In case \(X\) is 0-dimensional, he finds necessary and sufficient conditions on \(X\) so that (i) for all \(Y\), the Isbell and fine Isbell topologies on \(C(X, Y)\) coincide; (ii) the Isbell and fine Isbell topologies coincide on \(C(X, R)\), where \(R\) denotes the real numbers. A number of open problems are also cited.
reviewed by: James V. Whittaker
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 5791180
zbMATH Keywords: Isbell topology
zbMATH Keywords: finest splitting topology
zbMATH Keywords: compact family splittable
zbMATH Keywords: consonant space
MaRDI profile type: Publication
full work available at URL: j.topol.2010.07.007
OpenAlex ID: W2022838626
cites work: When do the Upper Kuratowski Topology (Homeomorphically, Scott Topology) and the Co-compact Topology Coincide?
cites work: Group topologies coarser than the Isbell topology
cites work: When is the Isbell topology a group topology?
cites work: Q5520521
cites work: Q4819380
cites work: Q3270120
cites work: Coincidence of function space topologies
cites work: When does the Fell topology on a hyperspace of closed sets coincide with the meet of the upper Kuratowski and the lower Vietoris topologies?
DOI: 10.1016/J.TOPOL.2010.07.007
description: scientific article; zbMATH DE number 5791180