Publication detail
The de Groot dual for general collections of sets
KOVÁR, M.
Original Title
The de Groot dual for general collections of sets
Type
conference paper
Language
English
Original 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.
Key words in English
saturated set, dual topology, compactness operator
Authors
KOVÁR, M.
RIV year
2004
Released
14. 10. 2004
Publisher
IBFI Schloss Dagstuhl
Location
Schloss Dagstuhl, Deutschland
Pages from
1
Pages to
8
Pages count
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"
}