Porosity properties of perturbed Cantor sets
Volume 166 / 2021
Colloquium Mathematicum 166 (2021), 313-333
MSC: 28A75, 26A03, 28A05, 51F99.
DOI: 10.4064/cm8314-9-2021
Published online: 29 September 2021
Abstract
We study perturbed Cantor subsets of $[0,1]$ which, in the general case, differ in some respects from central Cantor sets. We focus on their porosity properties. We obtain sufficient conditions for a perturbed Cantor set to be porous (or strongly porous). We establish the exact values of upper one-sided porosities at certain points with periodic addresses of special perturbed Cantor sets.
