A survey that reviews Borel hierarchy and four representations of Cantor sets, gives explicit descriptions for thin zero-measure and positive-measure families, shows the middle-third set belongs to all three families, and isolates open problems.
Julia Sets and wild Cantor sets
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abstract
There exist uniformly quasiregular maps $f:\mathbb{R}^3 \to \mathbb{R}^3$ whose Julia sets are wild Cantor sets.
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math.CA 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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Descriptions of Cantor Sets: A Set-Theoretic Survey and Open Problems
A survey that reviews Borel hierarchy and four representations of Cantor sets, gives explicit descriptions for thin zero-measure and positive-measure families, shows the middle-third set belongs to all three families, and isolates open problems.