A Solution of Problem 540
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F01%3APU22440" target="_blank" >RIV/00216305:26220/01:PU22440 - 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
A Solution of Problem 540
Original language description
Problem 540 of J. D. Lawson and M. Mislove in Open Problems in Topology asks whether the process of taking duals terminate after finitely many steps with topologies that are duals of each other. The problem was for $T_1$ spaces already solved by G. E. Strecker in 1966. For certain topologies on hyperspaces (which are not necessarily $T_1$), the main question was in the positive answered by Bruce S. Burdick and his solution was presented on The First Turkish International Confereence on Topology in Istanbul in 2000. In this paper we bring a complete and positive solution of the problem for all topological spaces. We show that for any topological space $(X,tau)$ it follows $tau^{dd}=tau^{dddd}$. Further, we classify topological spaces with respect tothe number of generated topologies by the process of taking duals.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
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
Name of the periodical
Topology Atlas, Questions & Answers, Topology Atlas Document # idec-33, http://at.yorku.ca/i/d/e/c/33.htm
ISSN
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e-ISSN
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Volume of the periodical
2001
Issue of the periodical within the volume
470
Country of publishing house
CA - CANADA
Number of pages
7
Pages from-to
1-7
UT code for WoS article
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EID of the result in the Scopus database
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