  In one of our previous papers we proved that, for an infinite set A and
p\in[1,\infty), the embedded version of the Lipscomb's space L(A) in l^{p}(A),
p\in[1,\infty), with the metric induced from l^{p}(A), denoted by
{\omega}_{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 {\omega}_{p}^{A}={\omega}_{q}^{A}, for all p,q\in[1,\infty) and, by
providing a complete description of the convergent sequences from
{\omega}_{p}^{A}, we prove that the topological structure of {\omega}_{p}^{A}
is independent of p.
