The independence of p of the Lipscombʼs L(A) space fractalized in lp(A)

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 lp(A), p∈[1,∞), with the metric induced from lp(A), denoted by , is the attractor of an infinite iterated function system comprising affine transformations of lp(A). In the present paper we point out that , for all p,q∈[1,∞) and, by providing a complete description of the convergent sequences from , we prove that the topological structure of is independent of p.