Publication detail

# On iterated dualizations of topological spaces and structures

KOVÁR, M.

Original Title

On iterated dualizations of topological spaces and structures

English Title

On iterated dualizations of topological spaces and structures

Type

conference paper

Language

en

Original Abstract

Recall that a topology $\tau^d$ is said to be dual with respect to the topology $\tau$ on a set $X$ if $\tau^d$ has a closed base consisted of the compact saturated sets in $\tau$. In the well-known book{\it Open Problems in Topology}, edited by J. van Mill and G. M. Reed, there was stated (among many others, no less interesting problems) a problem no. 540 of J. D. Lawson and M. Mislove: {\it Does the process of iterating duals of a topology terminate by two topologies, dual to each other (1990, \cite{LM})?} In this paper we will present some recent results related to iterated dualizations of topological spaces (one of them yields the above mentioned identity $\tau^{dd}=\tau^{dddd}$ as an immediate consequence), ask what happens with the dualizations if we leave the realm of spatiality and mention some unsolved problems related to dual topologies.

English abstract

Recall that a topology $\tau^d$ is said to be dual with respect to the topology $\tau$ on a set $X$ if $\tau^d$ has a closed base consisted of the compact saturated sets in $\tau$. In the well-known book{\it Open Problems in Topology}, edited by J. van Mill and G. M. Reed, there was stated (among many others, no less interesting problems) a problem no. 540 of J. D. Lawson and M. Mislove: {\it Does the process of iterating duals of a topology terminate by two topologies, dual to each other (1990, \cite{LM})?} In this paper we will present some recent results related to iterated dualizations of topological spaces (one of them yields the above mentioned identity $\tau^{dd}=\tau^{dddd}$ as an immediate consequence), ask what happens with the dualizations if we leave the realm of spatiality and mention some unsolved problems related to dual topologies.

RIV year

2002

Released

03.05.2002

Publisher

City College, City University of New York

Location

New York, Spojené státy americké

Pages from

11

Pages to

12

Pages count

2

Documents

BibTex


@inproceedings{BUT5184,
author="Martin {Kovár}",
title="On iterated dualizations of topological spaces and structures",
annote="Recall that a topology $\tau^d$ is said to be dual with respect to the topology $\tau$ on a set $X$ if $\tau^d$ has a closed base consisted
of the compact saturated sets in $\tau$.
In the well-known book{\it Open Problems in Topology}, edited by J.  van Mill and  G. M. Reed, there was stated
(among many others, no less interesting problems)  a problem no. 540 of  J. D. Lawson and M. Mislove: {\it Does the process
of iterating duals of a topology terminate by two topologies, dual to each other (1990, \cite{LM})?}

In this paper we will present some recent results related to iterated dualizations of topological spaces (one of them yields the above mentioned identity $\tau^{dd}=\tau^{dddd}$ as an immediate consequence), ask what happens with the dualizations if we leave the realm of spatiality
and mention some unsolved problems related to dual topologies.

",
address="City College, City University of New York",
booktitle="Abstracts of the Workshop on Topology in Computer Science",
chapter="5184",
institution="City College, City University of New York",
year="2002",
month="may",
pages="11",
publisher="City College, City University of New York",
type="conference paper"
}