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Publication detail
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
RIV year
2004
Released
14. 10. 2004
Publisher
IBFI Schloss Dagstuhl
Location
Schloss Dagstuhl, Deutschland
Pages from
1
Pages to
8
Pages count
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" }