Topological and measure properties of some self-similar sets

Taras Banakh, Artur Bartoszewicz, Emilia Szymonik, Małgorzata Filipczak
2015 Topological Methods in Nonlinear Analysis  
Given a finite subset Σ ⊂ R and a positive real number q < 1 we study topological and measure-theoretic properties of the self-similar set K(Σ; q) = ∞ n=0 anq n : (an)n∈ω ∈ Σ ω , which is the unique compact solution of the equation K = Σ + qK. The obtained results are applied to studying partial sumsets E(x) = ∞ n=0 xnεn : (εn)n∈ω ∈ {0, 1} ω of multigeometric sequences x = (xn)n∈ω. Such sets were investigated by Ferens, Morán, Jones and others. The aim of the paper is to unify and deepen
more » ... y and deepen existing piecemeal results.
doi:10.12775/tmna.2015.075 fatcat:wglvae4stna6rf5sicje5unxpm