Detail publikace

The de Groot dual for general collections of sets

Originální název

The de Groot dual for general collections of sets

Anglický název

The de Groot dual for general collections of sets

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

BibTex


@inproceedings{BUT11708,
  author="Martin {Kovár}",
  title="The de Groot dual for general collections of sets",
  annote="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.",
  address="IBFI  Schloss Dagstuhl",
  booktitle="Proceedings of the Dagstuhl Seminar 04351 - Spatial Representation: Discrete vs. Continuous Computational Models",
  chapter="11708",
  institution="IBFI  Schloss Dagstuhl",
  number="04351",
  year="2004",
  month="october",
  pages="1",
  publisher="IBFI  Schloss Dagstuhl",
  type="conference paper"
}