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.
Twofold Cantor sets in R
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abstract
We introduce a class of self-similar sets which we call {\em twofold Cantor sets} $K_{pq}$ in $\mathbb R$ which are totally disconnected, do not have weak separation property and at the same time have isomorphic self-similar structures.
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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.