Lipscomb’s space 𝜔^{𝐴} is the attractor of an infinite IFS containing affine transformations of 𝑙²(𝐴)

Miculescu, Radu; Mihail, Alexandru

doi:10.1090/S0002-9939-07-08981-2

Lipscomb’s space $\omega ^{A}$ is the attractor of an infinite IFS containing affine transformations of $l^{2}(A)$
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by Radu Miculescu and Alexandru Mihail PDF

Proc. Amer. Math. Soc. 136 (2008), 587-592 Request permission

Abstract:

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.

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