Topological classification of scattered IFS-attractors

Magdalena Nowak

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arXiv · 1204.4797

Topological classification of scattered IFS-attractors

Magdalena Nowak

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Abstract

We study countable compact spaces as potential attractors of iterated function systems. We give an example of a convergent sequence in the real line which is not an IFS-attractor and for each countable ordinal $\delta$ we show that a countable compact space of height $\delta+1$ can be embedded in the real line so that it becomes the attractor of an IFS. On the other hand, we show that a scattered compact metric space of limit height is never an IFS-attractor.

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Magdalena Nowak. 2012-04-21. Topological classification of scattered IFS-attractors. https://arxiv.org/abs/1204.4797

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