Lipscomb's space $\omega^{A}$ is the attractor of an infinite IFS containing affine transformations of $l^{2}(A)$

It is known that Lipscomb's space $L(A)$ can be imbedded in Hilbert's space $l^{2}(A)$. Let $\omega ^{A}$ be the imbedded version of $L(A)$ endowed with the $l^{2}(A)$-induced topology. We show how to construct $\omega ^{A}$ as the attractor of an iterated function system containing an infinite number of affine transformations of $l^{2}(A)$. In this way we answer an open question of J.C. Perry.