Result Details
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.
@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"
}