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  • A topology is de Groot dual of another topology, if it has a closed base consisting of all its compact saturated sets. Until 2001 it was an unsolved problem of J. Lawson and M. Mislove whether the sequence of iterated dualizations of a topological space is finite. In this paper we generalize the author's original construction to an arbitrary family instead of a topology. Among other results we prove that for any family $\C\subseteq 2^X$ it holds $\C^{dd}=\C^{dddd}$. We also show similar identities for some other similar and topology-related structures.
  • A topology is de Groot dual of another topology, if it has a closed base consisting of all its compact saturated sets. Until 2001 it was an unsolved problem of J. Lawson and M. Mislove whether the sequence of iterated dualizations of a topological space is finite. In this paper we generalize the author's original construction to an arbitrary family instead of a topology. Among other results we prove that for any family $\C\subseteq 2^X$ it holds $\C^{dd}=\C^{dddd}$. We also show similar identities for some other similar and topology-related structures. (en)
Title
  • The de Groot dual for general collections of sets
  • The de Groot dual for general collections of sets (en)
skos:prefLabel
  • The de Groot dual for general collections of sets
  • The de Groot dual for general collections of sets (en)
skos:notation
  • RIV/00216305:26220/04:PU46314!RIV11-MSM-26220___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • N, P(GA201/03/0933), V, Z(MSM 262200012)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 559477
http://linked.open...ai/riv/idVysledku
  • RIV/00216305:26220/04:PU46314
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • saturated set, dual topology, compactness operator (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [10AA3BC09158]
http://linked.open...v/mistoKonaniAkce
  • Dagstuhl
http://linked.open...i/riv/mistoVydani
  • Schloss Dagstuhl, Deutschland
http://linked.open...i/riv/nazevZdroje
  • Proceedings of the Dagstuhl Seminar 04351 - Spatial Representation: Discrete vs. Continuous Computational Models
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Kovár, Martin
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
http://linked.open...n/vavai/riv/zamer
number of pages
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  • IBFI Schloss Dagstuhl
http://localhost/t...ganizacniJednotka
  • 26220
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