Topology Proceedings 30 No. 1 (2006), pp. 69-81

Twisted Solenoids and Maps of R² Whose Minimal Sets Are Cantor Sets

William Basener and Carl V. Lutzer

We construct homeomorphisms of R² that have a minimal Cantor set similar to cross sections to solenoids. It is proven that certain of these homeomorphisms are C^∞ and the rest are not continuously differentiable. The differentiability depends on the number of components of the n^th stage in the construction of the Cantor set.

Keywords: minimal set, solenoid

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Topology Proceedings, Volume 30, No. 1 (2006)
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Twisted Solenoids and Maps of R2 Whose Minimal Sets Are Cantor Sets

William Basener and Carl V. Lutzer

Twisted Solenoids and Maps of R² Whose Minimal Sets Are Cantor Sets