On iterated dualizations of topological structures

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F02%3APU30316" target="_blank" >RIV/00216305:26220/02:PU30316 - 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 structures

Popis výsledku v původním jazyce

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 consisting of the compact saturated sets in the topological space $(X,tau)$. In the well-known book{it Open Problems in Topology}, edited by J. van Mill and G. M. Reed, there was stated the 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})?} As a matter of fact, for $T_1$ spaces, the problem was solved by G. E. Strecker, J. de Groot and E. Wattel (1966, cite{GSW}) a long time before it was formulated by Lawson and Mislove, since in $T_1$ spaces, the dual operator studied by Lawson and Mislove coincides with another dual, introduced by de Groot, Strecker and Wattel more than 30 years ago. In 2000 the problem was partially solved by B. Burdick, who proved that for some topologies on certain hyperspaces, during the iterated dualization process

Název v anglickém jazyce

On iterated dualizations of topological structures

Popis výsledku anglicky

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 consisting of the compact saturated sets in the topological space $(X,tau)$. In the well-known book{it Open Problems in Topology}, edited by J. van Mill and G. M. Reed, there was stated the 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})?} As a matter of fact, for $T_1$ spaces, the problem was solved by G. E. Strecker, J. de Groot and E. Wattel (1966, cite{GSW}) a long time before it was formulated by Lawson and Mislove, since in $T_1$ spaces, the dual operator studied by Lawson and Mislove coincides with another dual, introduced by de Groot, Strecker and Wattel more than 30 years ago. In 2000 the problem was partially solved by B. Burdick, who proved that for some topologies on certain hyperspaces, during the iterated dualization process

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

Abstract of the International Conference on Topology and Its Applications - Topology in Matsue

ISBN

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ISSN

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e-ISSN

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Počet stran výsledku

2

Strana od-do

42-43

Název nakladatele

Shimane University in Matsue Osaka university

Místo vydání

Matsue, Japonsko

Místo konání akce

Matsue

Datum konání akce

24. 6. 2002

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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