Abstract
Given r ∈ [0, 1] we study descriptive complexity of the set P r (respectively D r) of all compact sets K in the hyperspace \( \mathcal{K} \)(R) with porosity r (density r) at 0. We also show that the set NBP of all nowhere bilaterally porous compact sets in \( \mathcal{K} \)(R) is Π 11 -complete, and we prove a similar fact for density.
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Supported by the Polish Ministery of Science and Higher Education Grant No. 1P03A02330.
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Gła̧b, S. Descriptive properties related to porosity and density for compact sets on the real line. Acta Math Hung 116, 61–71 (2007). https://doi.org/10.1007/s10474-007-5291-7
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DOI: https://doi.org/10.1007/s10474-007-5291-7