Detail publikačního výsledku

The de Groot dual for general collections of sets

KOVÁR, M.

Originální název

The de Groot dual for general collections of sets

Anglický název

The de Groot dual for general collections of sets

Druh

Stať ve sborníku v databázi WoS či Scopus

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.

Klíčová slova v angličtině

saturated set, dual topology, compactness operator

Autoři

KOVÁR, M.

Rok RIV

2011

Vydáno

14.10.2004

Nakladatel

IBFI Schloss Dagstuhl

Místo

Schloss Dagstuhl, Deutschland

Kniha

Proceedings of the Dagstuhl Seminar 04351 - Spatial Representation: Discrete vs. Continuous Computational Models

Svazek

1

Číslo

04351

Strany od

1

Strany počet

8

URL

ftp://ftp.dagstuhl.de/pub/Proceedings/04/04351/04351.KovarMartin5.Paper!.pdf

BibTex

@inproceedings{BUT11708,
  author="Martin {Kovár}",
  title="The de Groot dual for general collections of sets",
  booktitle="Proceedings of the Dagstuhl Seminar 04351 - Spatial Representation: Discrete vs. Continuous Computational Models",
  year="2004",
  volume="1",
  number="04351",
  pages="8",
  publisher="IBFI  Schloss Dagstuhl",
  address="Schloss Dagstuhl, Deutschland",
  url="ftp://ftp.dagstuhl.de/pub/Proceedings/04/04351/04351.KovarMartin5.Paper!.pdf"
}