When the weak separation condition implies the generalized finite type condition

Hare, Kathryn; Hare, Kevin; Rutar, Alex

doi:10.1090/proc/15307

When the weak separation condition implies the generalized finite type condition
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by Kathryn E. Hare, Kevin G. Hare and Alex Rutar PDF

Proc. Amer. Math. Soc. 149 (2021), 1555-1568 Request permission

Abstract:

We prove that an iterated function system of similarities on $\mathbb {R}$ that satisfies the weak separation condition and has an interval as its self-similar set is of generalized finite type. It is unknown if the assumption that the self-similar set is an interval is necessary.

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