Detail publikace

On iterated dualizations of topological spaces and structures

KOVÁR, M.

Originální název

On iterated dualizations of topological spaces and structures

Typ

článek ve sborníku ve WoS nebo Scopus

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova v angličtině

compact saturated set, dual topology, topological system, frame, locale, directly complete semilattice

Autoři

KOVÁR, M.

Rok RIV

2002

Vydáno

3. 5. 2002

Nakladatel

City College, City University of New York

Místo

New York, Spojené státy americké

Strany od

11

Strany do

12

Strany počet

2

BibTex

@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"
}