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AuthorGarity, Dennis
Repovš, Dušan, 1954-
Željko, Matjaž
Title Rigid Cantor sets in R[sup]3 with simply connected complement / Dennis Garity, Dušan Repovš, Matjaž Željko
Type/contenttype of material article - component part
Publication date2006
Physical descriptionstr. 2447-2456
NotesBibliografija: str. 2455-2456
Uncontrolled subject headingsmatematika / topologija / divja Cantorjeva množica / toga množica / lokalni rod / definicijsko zaporedje / mathematics / topology / wild Cantor set / rigid set / local genus / defining sequence
Other class numbers
57N10 (MSC 2000)
SummaryWe prove that there exist uncountably many inequivalent rigid wild Cantor sets in $\RR^3$ with simply connected complement. Previous constructions of wild Cantor sets in $\RR^3$ with simply connected complement, in particular the Bing-Whitehead Cantor sets, had strong homogeneity properties. This suggested it might not be possible to construct such set that were rigid. The examples in this paper are constructed using a generalization of a construction of Skora together with a careful analysis of the local genus of points in the Cantor sets.
See publication: TI=Proceedings of the American Mathematical Society ISSN: 0002-9939.- Vol. 134, no. 8 (2006), str. 2447-2456