Abstract

We show that the space called the shark teeth is a topological IFS-attractor, that is, for every open cover of \(X = \bigcup\nolimits_{i = 1}^n {f_i (X)}\), its image under every suitable large composition from the family of continuous functions {f 1, ..., f n } lies in some set from the cover. In particular, there exists a space that is not homeomorphic to any IFS-attractor but is a topological IFS-attractor.

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