Visibility of Cartesian Products of Cantor Sets

Abstract

Let [Formula: see text] be the attractor of the following iterated function system(IFS): [Formula: see text] Given [Formula: see text], we say the line [Formula: see text] is visible through [Formula: see text] if [Formula: see text] Let [Formula: see text]. In this paper, we give a complete description of [Formula: see text], containing its Hausdorff dimension and topological properties.