Abstract
Most compact sets have small Hausdorff and lower entropy dimension, large upper entropy dimension, each of their points is “almost isolated” and they are “very porous”. Similar statements hold for continua, continuous curves and graphs of real continuous functions.
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Dedicated to Professor Leopold Schmetterer on the occasion of his 70th birthday
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Gruber, P.M. Dimension and structure of typical compact sets, continua and curves. Monatshefte für Mathematik 108, 149–164 (1989). https://doi.org/10.1007/BF01308668
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DOI: https://doi.org/10.1007/BF01308668