On iterated dualizations of topological spaces and structures

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F02%3APU30314" target="_blank" >RIV/00216305:26220/02:PU30314 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On iterated dualizations of topological spaces and structures

Popis výsledku v původním jazyce

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 (19900, 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 dualizationsif we leave the realm of spatiality and mention some unsolved problems related to dual topologies.

Název v anglickém jazyce

On iterated dualizations of topological spaces and structures

Popis výsledku anglicky

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 (19900, 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 dualizationsif we leave the realm of spatiality and mention some unsolved problems related to dual topologies.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F00%2F1466" target="_blank" >GA201/00/1466: Spojité a teoreticko-množinové metody v topologických a algebraických strukturách</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2002

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Abstracts of the Workshop on Topology in Computer Science

ISBN

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ISSN

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e-ISSN

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Počet stran výsledku

2

Strana od-do

11-12

Název nakladatele

City College, City University of New York

Místo vydání

New York, Spojené státy americké

Místo konání akce

New York

Datum konání akce

3. 5. 2002

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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