The shark teeth is a topological IFS-attractor

Abstract

We show that the space called shark teeth is a topological IFS-attractor, that is for every open cover of $X=\bigcup_{i=1}^nf_i(X)$, 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 which is not homeomorphic to any IFS-attractor but is a topological IFS-attractor.