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AuthorŽeljko, Matjaž
Title Genus of a Cantor set / Matjaž Željko
Other titlesRod Cantorjeve množice
Type/contenttype of material article - component part
LanguageEnglish
Publication date2005
Physical descriptionstr. 349-366
NotesBibliografija: str. 366
Uncontrolled subject headingsmatematika / topologija / Cantorjeva množica / definicijska zaporedja / rod / lastnost 1-ULC / mathematics / topology / Cantor set / defining sequences / genus / 1-ULC property
UDC515.162.6
Other class numbers
57M30 (MSC 2000)
SummaryRod Cantorjeve množice definiramo kot minimalno število največjega števila ročajev pri vseh možnih definicijskih zaporedjih za to množico. V članku obravnavamo zvezo med lokalnim in globalnim rodom v promeru roda 0 ali 1. Dokažemo kriterij za oceno lokalnega roda in konstruiramo primer Cantorjeve množice predpisanega roda. Dokažemo tudi, da pogoj, podoben pogoju 1-ULC, implicira, da je lokalni rod enak 0.
We define a genus of a Cantor set as a minimal number of the maximal number of handles over all possible defining sequences for it. The relationship between the local and the global genus is studied for genus 0 and 1. The criterion for estimating local genus is proved along with the example of Cantor set having prescribed genus. It is shown that some condition similar to 1-ULC implies local genus equal to 0.
COBISS.SI-ID13485145
See publication: TI=Rocky Mountain journal of mathematics ISSN: 0035-7596.- Vol. 35, no. 1 (2005), str. 349-366