The de Groot dual for general collections of sets

Author Martin Kovar



PDF
Thumbnail PDF

File

DagSemProc.04351.19.pdf
  • Filesize: 208 kB
  • 8 pages

Document Identifiers

Author Details

Martin Kovar

Cite AsGet BibTex

Martin Kovar. The de Groot dual for general collections of sets. In Spatial Representation: Discrete vs. Continuous Computational Models. Dagstuhl Seminar Proceedings, Volume 4351, pp. 1-8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)
https://doi.org/10.4230/DagSemProc.04351.19

Abstract

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.
Keywords
  • Saturated set
  • dual topology
  • compactness operator

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads