Problem 540 is (almost) solved
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F01%3APU22663" target="_blank" >RIV/00216305:26220/01:PU22663 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
Problem 540 is (almost) solved
Original language description
Recall that a set is said to be saturated if it is the intersection of open sets. By the dual topology $tau^d$ for a topological space $(X,tau)$ we mean the topology on $X$ generated by taking the compact saturated sets of $X$ as a subbase for closed sets. The Problem 540 of J. D. Lawson and M. Mislove cite{LM} in Open Problems in Topology (J. van Mill, G. M. Reed, eds.,1990) asks medskip roster item which topologies can arise as dual topologies smallskip and smallskipp item whether the processof taking duals terminate after finitely many steps with the topologies that are duals of each other. endroster medskip For $T_1$ spaces, the solution of (2) simply follows from the fact that in $T_1$ spaces every set is saturated and hence the dual operator $d$ coincide with the compactness operator $rho $ of J. de Groot, G. E. Strecker and E. Wattel cite{GSW}. For more general spaces, the question (2) was partially answered by Bruce S. B
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
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)
Others
Publication year
2001
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Abstracts of the Ninth Prague Topological Symposium
ISBN
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ISSN
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e-ISSN
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Number of pages
2
Pages from-to
45-46
Publisher name
Matematicko-fyzikální fakulta Univerzity Karlovy
Place of publication
Neuveden
Event location
Praha
Event date
Aug 19, 2001
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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