About: Problem 540 is (almost) solved

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: Problem 540 is (almost) solved Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Recall that a set is said to be saturated if it is the intersection of open sets. By the dual topology $\tau^d$ for a topological space $(X,\tau)$ we mean the topology on $X$ generated by taking the compact saturated sets of $X$ as a subbase for closed sets. The Problem 540 of J. D. Lawson and M. Mislove \cite{LM} in Open Problems in Topology (J. van Mill, G. M. Reed, eds.,1990) asks \medskip \roster \item which topologies can arise as dual topologies \smallskip and \smallskipp \item whether the process of taking duals terminate after finitely many steps with the topologies that are duals of each other. \endroster \medskip For $T_1$ spaces, the solution of (2) simply follows from the fact that in $T_1$ spaces every set is saturated and hence the dual operator $d$ coincide with the compactness operator $\rho $ of J. de Groot, G. E. Strecker and E. Wattel \cite{GSW}. For more general spaces, the question (2) was partially answered by Bruce S. B Recall that a set is said to be saturated if it is the intersection of open sets. By the dual topology $\tau^d$ for a topological space $(X,\tau)$ we mean the topology on $X$ generated by taking the compact saturated sets of $X$ as a subbase for closed sets. The Problem 540 of J. D. Lawson and M. Mislove \cite{LM} in Open Problems in Topology (J. van Mill, G. M. Reed, eds.,1990) asks \medskip \roster \item which topologies can arise as dual topologies \smallskip and \smallskipp \item whether the process of taking duals terminate after finitely many steps with the topologies that are duals of each other. \endroster \medskip For $T_1$ spaces, the solution of (2) simply follows from the fact that in $T_1$ spaces every set is saturated and hence the dual operator $d$ coincide with the compactness operator $\rho $ of J. de Groot, G. E. Strecker and E. Wattel \cite{GSW}. For more general spaces, the question (2) was partially answered by Bruce S. B (en)
Title	Problem 540 is (almost) solved Problem 540 is (almost) solved (en)
skos:prefLabel	Problem 540 is (almost) solved Problem 540 is (almost) solved (en)
skos:notation	RIV/00216305:26220/01:PU22663!RIV/2002/GA0/262202/N
http://linked.open.../vavai/riv/strany	45-46
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/00/1466), Z(MSM 262200012)
http://linked.open...vai/riv/dodaniDat	2002
http://linked.open...aciTvurceVysledku	Kovár, Martin
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Vysoké učení technické v Brně / Fakulta elektrotechniky a komunikačních technologií
http://linked.open...dnocenehoVysledku	692962
http://linked.open...ai/riv/idVysledku	RIV/00216305:26220/01:PU22663
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	saturated set, order of specialization, dual topology, compactness operator (en)
http://linked.open.../riv/klicoveSlovo	compactness operator dual topology saturated set order of specialization
http://linked.open...ontrolniKodProRIV	[FB3909F22A01]
http://linked.open...v/mistoKonaniAkce	Praha
http://linked.open...i/riv/mistoVydani	Neuveden
http://linked.open...i/riv/nazevZdroje	Abstracts of the Ninth Prague Topological Symposium
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...ocetUcastnikuAkce	0 (xsd:int)
http://linked.open...nichUcastnikuAkce	0 (xsd:int)
http://linked.open...vavai/riv/projekt	Continuous and set-theoretical methods in topological and algebraic structures
http://linked.open...UplatneniVysledku	2001
http://linked.open...iv/tvurceVysledku	Kovár, Martin
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2001-08-19 (xsd:date)
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20262200012
number of pages	2 (xsd:int)
http://purl.org/ne...btex#hasPublisher	Univerzita Karlova v Praze. Matematicko-fyzikální fakulta
http://localhost/t...ganizacniJednotka	26220

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 58 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software