About: The structure of Valdivia compact lines

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed 8(1), every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author. We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed 8(1), every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author. (en)
Title	The structure of Valdivia compact lines The structure of Valdivia compact lines (en)
skos:prefLabel	The structure of Valdivia compact lines The structure of Valdivia compact lines (en)
skos:notation	RIV/67985840:_____/10:00342854!RIV11-AV0-67985840
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/06/0018), P(IAA100190901), Z(AV0Z10190503), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	7
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Kubiś, Wieslaw
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Matematický ústav AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	290520
http://linked.open...ai/riv/idVysledku	RIV/67985840:_____/10:00342854
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	valdivia compact line; increasing map; retraction (en)
http://linked.open.../riv/klicoveSlovo	retraction increasing map valdivia compact line
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[2B013ED8BC34]
http://linked.open...i/riv/nazevZdroje	Topology and its Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Topological and geometric structures in Banach spaces Topological structures in functional analysis
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	157
http://linked.open...iv/tvurceVysledku	Kubiś, Wieslaw Kalenda, O. F. K.
http://linked.open...ain/vavai/riv/wos	000276840900004
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi Metody moderní matematiky a jejich aplikace
issn	0166-8641
number of pages	10 (xsd:int)

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