When $K=[0,1]$ Weak Separation Condition coincides Finite type Condition

Abstract

This study is about the Iterated Function System (IFS) of similarities on $\mathbb{R}$ that satisfies Weak Separation property (WSP). We explore if this implies Finite type property. We look into the most simple case with condition that closed interval [0,1] is an attractor of the IFS. The necessity of this condition is not strict but still unknown.

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