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Hausdorff Dimension dimension vs. CardinalitycardinalityWhat is the relationship between the hausdorff Hausdorff dimension and cardinality of a set? Specifically, assuming the Continuum Hypothesis, if a set has Hausdorff dimension greater than zero does, that imply that its cardinality is equal too or greater than that of 2^Aleph_0? Or, does the negation of CH, imply the existence of a set with positive Hausdorff dimension and cardinality strictly between Aleph_0 and 2^Aleph_0? |
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What is the relationship between the hausdorff dimension and cardinality of a set? Specifically, assuming the Continuum Hypothesis, if a set has Hausdorff dimension greater than zero does, that imply that its cardinality is equal too or greater than that of 2^Aleph_0? Or, does the Continuumnegation of CH, imply the existence of a set with positive Hausdorff dimension and cardinality strictly between Aleph_0 and 2^Aleph_0? |
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What is the relationship between the hausdorff dimension and cardinality of a set? Specifically, assuming the Continuum Hypothesis, if a set has Hausdorff dimension greater than zero doesHD(S) > 0 , that imply Card(S) >= Aleph-1that its cardinality is equal too or greater than that of the Continuum? |
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