On iterated de Groot dualizations of topological spaces
type: Item
instance of: scholarly article
title: On iterated de Groot dualizations of topological spaces
zbMATH Open document ID: 1068.54003
author: Martin Maria Kovár
published in: Topology and its Applications
publication date: 2005-02-22T00:00:00Z
review text: In 2001 the author solved an open problem of J. D. Lawson and M. Mislove (Problem 540 in Open Problems in Topology) by showing that the process of taking (de Groot) duals terminates after finitely many steps with topologies that are duals of each other. In the present paper the author proves a new identity for dual topologies, namely that \(\tau^d=(\tau \vee \tau^{dd})^d\) . In addition, a solution to another open problem is also presented.
reviewed by: Maximilian Ganster
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54B99
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54E55
zbMATH DE Number: 2136456
zbMATH Keywords: saturated set
zbMATH Keywords: dual topology
zbMATH Keywords: compactness operator
MaRDI profile type: Publication
full work available at URL: j.topol.2003.01.002
OpenAlex ID: W1967943226
cites work: Q5550369
cites work: Asymmetry and duality in topology
cites work: At most 4 topologies can arise from iterating the de Groot dual
cites work: Q3998752
DOI: 10.1016/J.TOPOL.2003.01.002
description: scientific article; zbMATH DE number 2136456