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

Selected record permalink

AuthorŽeljko, Matjaž
Title On linking of Cantor sets / Matjaž Željko
Other titlesO spletanju Cantorjevih množic
Type/contenttype of material article - component part
LanguageEnglish
Publication date2006
Physical descriptionstr. 165-176
NotesBibliografija: str. 176
Uncontrolled subject headingsmatematika / topologija / geometrično spletanje / Cantorjeva množica / definicijsko zaporedje / toga Cantorjeva množica / mathematics / topology / geometric linking / Cantor set / defining sequence / rigid Cantor set
UDC515.162
Other class numbers
57M30 (MSC 2000)
SummaryV članku vpeljemo lastnost ${\cal L}$ za podmnožico mnogoterosti, ki nam omogoča, da prenesemo lastnost spletanja z mnogoterosti na to podmnožico. Dokažemo, da sta krogli z ročaji $M$ in $N$ spleteni natanko tedaj, ko sta podmnožici $X \subset {\rm Int} M$ in $Y \subset {\rm Int} N$, ki imata lastnost ${\cal L}$, spleteni. Predstavljen je kriterij, s pomočjo katerega pokažemo, da ima mnogo Cantorjevih množic, ki so eksplicitno podane z definicijskimi zaporedji, lastnost ${\cal L}$. Kot uporabo lastnosti ${\cal L}$ razširimo izrek o togih Cantorjevih množicah tako, da dopustimo nekoliko bolj komplicirane člene v njihovih definicijskih zaporedjih.
We introduce a property ${\cal L}$ for a subset of a manifold which enables us to pass the geometric linking property from the manifold to this subset. We prove that cubes with handles $M$ and $N$ are linked if and only if subsets $X \subset {\rm Int} M$ and $Y \subset {\rm Int} N$ having property ${\cal L}$ are linked. We present a criterion which shows us that many of known Cantor sets explicitly given by defining sequences have this propertry. As an application of the property ${\cal L}$ we extend the theorem on rigid Cantor sets thus allowing us slightly more complicated terms in their defining sequences.
COBISS.SI-ID14029657
See publication: TI=Glasnik matematički. Serija 3 ISSN: 0017-095X.- Vol. 41, no. 1 (2006), str. 165-176