A counterexample to the Karvatskyi--Pratsiovytyi conjecture concerning the achievement set of an intermediate series

Abstract

We found a counterexample to the conjecture of Karvatskyi and Pratsiovytyi concerning the topological type of the achievement set of an intermediate series (Proceedings of the International Geometry Center, 2023. https://doi.org/10.15673/pigc.v16i3.2519). This conjecture is based on an analogy with the squeeze theorem from calculus. We also proposed an improved version of the conjecture, which this counterexample does not refute.