Cartesian products of the Sierpiński carpet (and similar self-similar fractals) with itself at least twice do not attain their conformal dimension.
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2 Pith papers cite this work. Polarity classification is still indexing.
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Any local Lipschitz one set on the real line must be quasi-dense but not conversely, and every regular closed subset of a normed space is a local Lipschitz one set though the converse fails.
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Cartesian products of Sierpi\'nski carpets do not attain their conformal dimension
Cartesian products of the Sierpiński carpet (and similar self-similar fractals) with itself at least twice do not attain their conformal dimension.
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On local Lipschitz one sets
Any local Lipschitz one set on the real line must be quasi-dense but not conversely, and every regular closed subset of a normed space is a local Lipschitz one set though the converse fails.