Topological classification of scattered IFS-attractors |
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Authors: | Magdalena Nowak |
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Institution: | 1. Faculty of Mathematics and Computer Science, Jagiellonian University, ul. ?ojasiewicza 6, 30-348 Kraków, Poland;2. Institute of Mathematics, Jan Kochanowski University, ul. ?wi?tokrzyska 15, 25-406 Kielce, Poland |
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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 δ we show that a countable compact space of height δ+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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Keywords: | primary 28A80 secondary 54E40 54C50 54G12 |
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