This HTML5 document contains 43 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
n12http://localhost/temp/predkladatel/
n11http://linked.opendata.cz/resource/domain/vavai/riv/tvurce/
n9http://linked.opendata.cz/ontology/domain/vavai/
n5http://linked.opendata.cz/resource/domain/vavai/zamer/
n16http://linked.opendata.cz/resource/domain/vavai/vysledek/RIV%2F47813059%3A19610%2F10%3A%230000267%21RIV10-MSM-19610___/
shttp://schema.org/
skoshttp://www.w3.org/2004/02/skos/core#
n3http://linked.opendata.cz/ontology/domain/vavai/riv/
n2http://linked.opendata.cz/resource/domain/vavai/vysledek/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
n4http://linked.opendata.cz/ontology/domain/vavai/riv/klicoveSlovo/
n13http://linked.opendata.cz/ontology/domain/vavai/riv/duvernostUdaju/
xsdhhttp://www.w3.org/2001/XMLSchema#
n17http://linked.opendata.cz/ontology/domain/vavai/riv/jazykVysledku/
n15http://linked.opendata.cz/ontology/domain/vavai/riv/aktivita/
n18http://linked.opendata.cz/ontology/domain/vavai/riv/druhVysledku/
n14http://linked.opendata.cz/ontology/domain/vavai/riv/obor/
n10http://reference.data.gov.uk/id/gregorian-year/

Statements

Subject Item
n2:RIV%2F47813059%3A19610%2F10%3A%230000267%21RIV10-MSM-19610___
rdf:type
n9:Vysledek skos:Concept
dcterms:description
According to a well-known result, the collection of all omega-limit sets of a continuous map of the interval equipped with the Hausdorff metric is a compact metric space. In this paper, a similar result is proved for piecewise continuous maps with finitely many points of discontinuity, if the points of discontinuity are not periodic for any variant of the map. A variant of f is a map g coinciding with f at any point of continuity and being continuous from one side at any point of discontinuity. It is also shown that omega-limit sets of these maps are locally saturating, another property known for continuous maps. However, contrary to the situation for continuous maps, there are piecewise continuous maps having locally saturating sets which are not omega-limit sets. A condition implying that a locally saturating set is an omega-limit set is presented According to a well-known result, the collection of all omega-limit sets of a continuous map of the interval equipped with the Hausdorff metric is a compact metric space. In this paper, a similar result is proved for piecewise continuous maps with finitely many points of discontinuity, if the points of discontinuity are not periodic for any variant of the map. A variant of f is a map g coinciding with f at any point of continuity and being continuous from one side at any point of discontinuity. It is also shown that omega-limit sets of these maps are locally saturating, another property known for continuous maps. However, contrary to the situation for continuous maps, there are piecewise continuous maps having locally saturating sets which are not omega-limit sets. A condition implying that a locally saturating set is an omega-limit set is presented
dcterms:title
The space of omega-limit sets of piecewise continuous maps of the interval The space of omega-limit sets of piecewise continuous maps of the interval
skos:prefLabel
The space of omega-limit sets of piecewise continuous maps of the interval The space of omega-limit sets of piecewise continuous maps of the interval
skos:notation
RIV/47813059:19610/10:#0000267!RIV10-MSM-19610___
n3:aktivita
n15:Z
n3:aktivity
Z(MSM4781305904)
n3:cisloPeriodika
2-3
n3:dodaniDat
n10:2010
n3:domaciTvurceVysledku
n11:7698143
n3:druhVysledku
n18:J
n3:duvernostUdaju
n13:S
n3:entitaPredkladatele
n16:predkladatel
n3:idSjednocenehoVysledku
288928
n3:idVysledku
RIV/47813059:19610/10:#0000267
n3:jazykVysledku
n17:eng
n3:klicovaSlova
omega-limit set; Hausdorff metric; piecewise continuous map; interval map; compactness; locally saturating set
n3:klicoveSlovo
n4:omega-limit%20set n4:locally%20saturating%20set n4:interval%20map n4:compactness n4:Hausdorff%20metric n4:piecewise%20continuous%20map
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[6A9EA48D7611]
n3:nazevZdroje
Journal of Difference Equations and Applications
n3:obor
n14:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
3
n3:rokUplatneniVysledku
n10:2010
n3:svazekPeriodika
16
n3:tvurceVysledku
Hofbauer, Franz Smítal, Jaroslav Raith, Peter
n3:wos
000275127200012
n3:zamer
n5:MSM4781305904
s:issn
1023-6198
s:numberOfPages
16
n12:organizacniJednotka
19610