A note on iterated duals of certain topological spaces
type: Item
instance of: scholarly article
title: A note on iterated duals of certain topological spaces
zbMATH Open document ID: 1030.54006
DOI: 10.1016/S0304-3975(00)00414-X
author: Bruce S. Burdick
published in: Theoretical Computer Science
publication date: 2002-07-31T00:00:00Z
review text: A set is called \(\tau\)-saturated if it is the intersection of its neighborhoods; the topology \(\tau^d\) generated by the complements of \(\tau\)-saturated \(\tau\)-compact subsets of \(X\) is called the dual of the topology \(\tau\) on \(X\). It was known that for \(T_1\)-spaces the relation \(\tau^{dd}=\tau^{dddd}\) holds and the author proves as the main result that this relation holds not only for \(T_1\)-topologies. He adds that ``after this paper was accepted, Martin Kovář of the Technical University of Brno communicated to the author a proof that \(\tau^{dd}=\tau^{dddd}\) for all topologies''. However the paper contains some other results on iterated duals, too.
Mathematics Subject Classification ID: 54B17
Mathematics Subject Classification ID: 54E55
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54B99
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54A10
zbMATH DE Number: 1774096
zbMATH Keywords: dual topology
zbMATH Keywords: bitopological spaces
zbMATH Keywords: compact
zbMATH Keywords: hyperspaces
zbMATH Keywords: Scott topology
reviewed by: Aleksandr A. Ivanov
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1774096