Detail výsledku
On iterated dualizations of topological spaces and structures
Recall that a topology $\tau^d$ is said to be dual with respect to the topology $\tau$ on a set $X$ if $\tau^d$ has a closed base consisted
of the compact saturated sets in $\tau$.
In the well-known book{\it Open Problems in Topology}, edited by J. van Mill and G. M. Reed, there was stated
(among many others, no less interesting problems) a problem no. 540 of J. D. Lawson and M. Mislove: {\it Does the process
of iterating duals of a topology terminate by two topologies, dual to each other (1990, \cite{LM})?}
In this paper we will present some recent results related to iterated dualizations of topological spaces (one of them yields the above mentioned identity $\tau^{dd}=\tau^{dddd}$ as an immediate consequence), ask what happens with the dualizations if we leave the realm of spatiality
and mention some unsolved problems related to dual topologies.
compact saturated set, dual topology, topological system, frame, locale, directly complete semilattice
@inproceedings{BUT5184,
author="Martin {Kovár}",
title="On iterated dualizations of topological spaces and structures",
booktitle="Abstracts of the Workshop on Topology in Computer Science",
year="2002",
number="1",
pages="2",
publisher="City College, City University of New York",
address="New York, Spojené státy americké"
}