At most 4 topologies can arise from iterating the de Groot dual

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F03%3APU39213" target="_blank" >RIV/00216305:26220/03:PU39213 - 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
At most 4 topologies can arise from iterating the de Groot dual
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 for $T_1$ spaces was 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 Conferennce on Topology in Istanbul in 2000. In this paper we show that for any topological space $(X,tau)$ it follows $tau^{dd}=tau^{dddd}$. Further, we classify topological spaces with respect to the number of generated topologies by the process of taking duals.
Czech name
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Czech description
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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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Project
<a href="/en/project/GA201%2F03%2F0933" target="_blank" >GA201/03/0933: Set-theoretical and categorial methods in topological and algebraic structures</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2003
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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