Selectibility is not preserved under open light mappings between fans (Q2800390)

For a continuum (i.e., a nonempty compact connected metric space) \(X\), let \(C (X)\) denote the space of all subcontinua of \(X\) equipped with the Hausdorff metric. A continuum \(X\) is said to be selective if there exists a continuous mapping \(\sigma : C(X) \to X\) such that \(\sigma (A) \in A\) for each \(A \in C(X)\). A dendroid is an arcwise connected continuum in which the intersection of any two of its subcontinua is connected. A point \(p\) of a dendroid \(X\) is called a ramification point it it is the common endpoint of three (or more) arcs in \(X\) whose only common point is \(p\). A dendroid having exactly one ramification point is called a fan. In [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 26, 547--551 (1978; Zbl 0412.54018)], \textit{T. Maćkowiak} asked whether selectibility is preserved under open mappings between fans. More specifically, \textit{J. J. Charatonik} et al. [Diss. Math. 301, 86 p (1990; Zbl 0776.54025)] asked whether selectibility is invariant under the mappings of fans that are (1) open and light, (2) open, (3) confluent and light. For (3), the first and third authors and \textit{I. Puga} gave a counterexample in [Topol. Proc. 40, 91--98 (2012; Zbl 1271.54067)]. In this paper, the authors answer the question negatively by constructing a light open mapping on a selectible fan onto a nonselectible fan.