Try new release: COBISS+
 Shared database: COBIB.SI - Union bibliographic/catalogue database (No. of records: 5.075.292)

Selected record permalink

AuthorKarimov, Umed H.
Repovš, Dušan, 1954-
Željko, Matjaž
Title On unions and intersections of simply connected planar sets / U. H. Karimov, D. Repovš, M. Željko
Other titlesO unijah in presekih enostavno povezanih ravninskih množic
Type/contenttype of material article - component part
LanguageEnglish
Publication date2005
Physical descriptionstr. 239-245
NotesBibliografija: str. 244-245
Uncontrolled subject headingsmatematika / topologija / homološka sfera / homološki disk / živec pokritja / ravninski kontinuumi / Seifert-van Kampenov izrek / Molnarjev izrek / enostavno povezane ravninske množice / mathematics / topology / simply connested planar sets / planar continua / Helly-type theorem / Molnar's theorem / Seifert-van Kampen theorem
UDC515.125.5
Other class numbers
54F15
55N10
54D05 (MSC 2000)
SummaryDokažemo naslednja dva glavna rezultata: (1) Za vsako naravno število $m>1$ obstaja homološka 1-sfera $X$ v ${\mathbb R}^2$ in tako bazično pokritje ${\mathcal F} = \left\{ X_i \riht\}_{i=0}^{m}$ prostora $X$ s kompaktnimi acikličnimi množicami, da je unija vsake prave poddružine pokritja ${\mathcal F}$ aciklična; in (2) Naj bo ${\mathcal F} = \left\{ X_i \riht\}_{i=0}^{m}$, $m>1$, taka družina odprtih ali zaprtih acikličnih mmnožic v ${\mathbb R}^2$, da je unija poljubnih dveh elementov iz ${\mathcal F}$ povezana s potmi in unija poljubnih treh elementov iz ${\mathcal F}$ aciklična. Potem je presek vseh elementov iz ${\mathcal F}$ neprazen.
We construct several simple examples of planar compacta which show that without additional conditions, a theorem of Breen and a direct generalization of the Seifert-van Kampen theorem fail. We give answers to two conjectures of Bogatyi and a partial solution to his third conjecture. We give a counterexample to a statement in the classical survey paper by Danzer-Grünbaum-Klee, related to Molnár's result on intersections of simply connected planar sets.
COBISS.SI-ID13617753
See publication: TI=Monatshefte für Mathematik ISSN: 0026-9255.- Vol. 145, no. 3 (2005), str. 239-245