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AuthorGarity, Dennis
Repovš, Dušan, 1954-
Željko, Matjaž
Title Uncountably many inequivalent Lipschitz homogeneous Cantor sets in R[sup]3 / Dennis Garity, Dušan Repovš, Matjaž Željko
Other titlesNeštevno mnogo neekvivalentnih Lipschitzovo homogenih Cantorjevih množic v R [na] 3
Type/contenttype of material article - component part
LanguageEnglish
Publication date2005
Physical descriptionstr. 287-299
NotesBibliografija: str. 298-299
Uncontrolled subject headingsmatematika / topologija / divja Cantorjeva množica / Lipschitzova homogenost / podobnost / koeficient podobnosti / definicijsko zaporedje / mathematics / topology / wild Cantor set / Lipschitz homogeneity / similitude / coefficient of similarity / defining sequence / link invariant
UDC515.124.5
Other class numbers
54E45
54F65
57M30
57N10 (MSC 2000)
SummaryPrikazane so splošne tehnike za konstrukcijo Lipschitzovo homogenih Cantorjevih množic v ${\mathbb{R}}^3$. Te tehnike nam skupaj z invariantami spletov in znanimi rezultati o Antoinovih Cantorjevih množicah omogočajo konstrukcijo neštevno mnogo topološko neekvivalentnih divjih Cantorjevih množic v ${\mathbb{R}}^3$. Dobljene Cantorjeve množice imajo enako število komponent v vsakem členu definicijskega zaporedja in so Lipschitzovo homogene.
General techniques are developed for constructing Lipschitz homogeneous wild Cantor sets in ${\mathbb{R}}^3$. These techniques, along with Kauffman's version of the Jones polynomial and previous results on Antoine Cantor sets, are used to construct uncountably many topologically inequivalent such wild Cantor sets in ${\mathbb{R}}^3$. This use of three-dimensional finite link invariants to detect distinctness among wild Cantor sets is unexpected. These Cantor sets have the same Antoine graphs and are Lipschitz homogeneous. As a corollary, there are uncountably many topologically inequivalent Cantor sets with the same Antoine graph.
COBISS.SI-ID13788249
See publication: TI=Pacific journal of mathematics ISSN: 0030-8730.- Vol. 222, no. 2 (2005), str. 287-299