About: Sequence of dualizations of topological spaces is finite.

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About: Sequence of dualizations of topological spaces is finite. Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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 classifytopological spaces with respect to the number of generated topologies by the process of taking duals. 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 classifytopological spaces with respect to the number of generated topologies by the process of taking duals. (en) Obsahem práce je zejména důkaz, že druhá a čtvrtá de Grootova duální topologie libovolného topologického prostoru splývají. Dále práce obsahuje některé další výsledky o vlastnostech duálních topologií. (cs)
Title	Posloupnost dualizací topologických prostorů je konečná. (cs) Sequence of dualizations of topological spaces is finite. Sequence of dualizations of topological spaces is finite. (en)
skos:prefLabel	Posloupnost dualizací topologických prostorů je konečná. (cs) Sequence of dualizations of topological spaces is finite. Sequence of dualizations of topological spaces is finite. (en)
skos:notation	RIV/00216305:26220/02:PU22441!RIV06-GA0-26220___
http://linked.open.../vavai/riv/strany	181-188
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/00/1466), Z(MSM 262200012)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2006
http://linked.open...aciTvurceVysledku	Kovár, Martin
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Vysoké učení technické v Brně / Fakulta elektrotechniky a komunikačních technologií
http://linked.open...dnocenehoVysledku	663341
http://linked.open...ai/riv/idVysledku	RIV/00216305:26220/02:PU22441
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	saturated set, dual topology, compactness operator (en)
http://linked.open.../riv/klicoveSlovo	compactness operator dual topology saturated set
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[44A751FAFD4A]
http://linked.open...i/riv/nazevZdroje	Proceedings of The Prague Topological Symposium
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Continuous and set-theoretical methods in topological and algebraic structures
http://linked.open...UplatneniVysledku	2002
http://linked.open...v/svazekPeriodika	9
http://linked.open...iv/tvurceVysledku	Kovár, Martin
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20262200012
number of pages	8 (xsd:int)
https://schema.org/isbn	0-9730867-0-X
http://localhost/t...ganizacniJednotka	26220

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