VISIBILITY of CARTESIAN PRODUCTS of CANTOR SETS

Let Kλ be the attractor of the following iterated function system(IFS): {f1(x) = λx,f2(x) = λx + 1 - λ}, 0 < λ < 1/2. Given α ≥ 0, we say the line y = αx is visible through Kλ × Kλ if {(x,αx): x ℝ∖{0}}∩ (Kλ × Kλ) = ∅. Let V = {α ≥ 0: y = αx is visible through Kλ × Kλ}. In this paper, we give a complete description of V, containing its Hausdorff dimension and topological properties.