On iterated de Groot dualizations of topological spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F05%3APU47143" target="_blank" >RIV/00216305:26220/05:PU47143 - 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 de Groot dualizations of topological spaces
Original language description
Problem 540 of J. D. Lawson and M. Mislove in Open Problems in Topology ask whether the process of taking (de Groot) duals terminate after finitely many steps with topologies that are duals of each other. The question was solved in the positive by the author in 2001. In this paper we prove a new identity for dual topologies: $tau^d= (tauveetau^{dd})^d$ holds for every topological space $(X,tau)$. We also present a solution of another problem that was open till now -- we give an equivalent internalcharacterization of those spaces for which $tau=tau^{dd}$ and we also characterize the spaces satisfying the identities $tau^d=tau^{ddd}$, $tau=tau^{d}$ and $tau^d=tau^{dd}$.
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
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Continuities
V - Vyzkumna aktivita podporovana z jinych verejnych zdroju<br>N - Vyzkumna aktivita podporovana z neverejnych zdroju

Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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