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oai:drops-oai.dagstuhl.de:121 2024-03-06T11:05:52Z ddc:004 open_access

The de Groot dual for general collections of sets Kovar, Martin Saturated set dual topology compactness operator 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Martin Kovar 2005 Is Part Of Dagstuhl Seminar Proceedings, Volume 4351, Spatial Representation: Discrete vs. Continuous Computational Models (2005) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.04351.19 urn:nbn:de:0030-drops-1215 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.04351.19 eng https://creativecommons.org/licenses/by/4.0/legalcode