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AuthorŽeljko, Matjaž
Title On defining sequences for Cantor sets / Matjaž Željko
Other titlesO definicijskih zaporedjih za Cantorjeve množice
Type/contenttype of material article - component part
LanguageEnglish
Publication date2001
Physical descriptionstr. 321-325
NotesBibliografija: str. 325
Uncontrolled subject headingsmatematika / topologija / vložitve / Cantorjeve množice / definicijska zaporedja / inkompresibilnost / mathematics / topology / embeddings / Cantor sets / defining sequences / incompressibility
UDC515.162.6
Other class numbers
57M30 (MSC 2000)
SummaryCantorjeva množica ima lahko mnogo bistveno različnih definicijskih zaporedij in v splošnem ne obstaja način, kako izbrati pravega. Naravni pristop z zmanjševanjem števila ročajev ni primeren, če je komplement Cantorjeve množice preveč "lep" (npr. enostavno povezan). Pokazano je, da v definicijskem zaporedju ni odvečnih ročajev natanko tedaj, ko Cantorjeva množica zadošča nekoliko oslabljenemu 1-ULC pogoju.
Each Cantor set can have many essentialy different defining sequences and there is not canonical way to chose one. The natural approach of reducing the number of handles does not work if the complement of a given Cantor set is too nice (for example: simply connected). It is shown that there are no "unnnecessary handles" in the defining sequence of a given Cantor set if and only if the the Cantor set satisfied some weakened 1-ULC property.
COBISS.SI-ID10712153
See publication: TI=Topology and its Applications ISSN: 0166-8641.- Vol. 113, no. 1-3 (2001), str. 321-325