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  • Rigid Cantor sets in ▫$\mathbb R^3$▫ with simply connected complement
    Garity, Dennis, 1950- ; Repovš, Dušan, 1954- ; Željko, Matjaž, 1967-
    We prove that there exist uncountably many inequivalent rigid wild Cantor sets in ▫$\mathbb R^3$▫ with simply connected complement. Previous constructions of wild Cantor sets in ▫$\mathbb R^3$▫ 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.
    Vir: Proceedings of the American Mathematical Society. - ISSN 0002-9939 (Vol. 134, no. 8, 2006, str. 2447-2456)
    Vrsta gradiva - članek, sestavni del
    Leto - 2006
    Jezik - angleški
    COBISS.SI-ID - 13945689

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