On iterated dualizations of topological structures

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On iterated dualizations of topological structures
Original language description
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
Czech name
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Czech description
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Project
<a href="/en/project/GA201%2F00%2F1466" target="_blank" >GA201/00/1466: Continuous and set-theoretical methods in topological and algebraic structures</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2002
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
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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Number of pages
2
Pages from-to
42-43
Publisher name
Shimane University in Matsue Osaka university
Place of publication
Matsue, Japonsko
Event location
Matsue
Event date
Jun 24, 2002
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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