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arXiv · 1110.3168

The Independence of p of the Lipscomb's L(A) Space Fractalized in l^{p}(A)

Radu Miculescu·Alexandru Mihail
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Abstract

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 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\in[1,\infty) 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.

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Radu Miculescu, Alexandru Mihail. 2011-10-14. The Independence of p of the Lipscomb's L(A) Space Fractalized in l^{p}(A). https://arxiv.org/abs/1110.3168

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