The independence of p of the Lipscombʼs space fractalized in

In one of our previous papers we proved that, for an infinite set A and p ∈ [ 1 , ∞ ) , the embedded version of the Lipscombʼs space L ( A ) in l p ( A ) , p ∈ [ 1 , ∞ ) , with the metric induced from l p ( A ) , denoted by ω p A , is the attractor of an infinite iterated function system comprising affine transformations of l p ( A ) . In the present paper we point out that ω p A = ω q A , for all p , q ∈ [ 1 , ∞ ) and, by providing a complete description of the convergent sequences from ω p A , we prove that the topological structure of ω p A is independent of p.