Property of being semi-Kelley for the cartesian products and hyperspaces

summary:In this paper we construct a Kelley continuum $X$ such that $X\times [0,1]$ is not semi-Kelley, this answers a question posed by J.J. Charatonik and W.J. Charatonik in A weaker form of the property of Kelley, Topology Proc. 23 (1998), 69--99. In addition, we show that the hyperspace $C(X)$ is not semi- Kelley. Further we show that small Whitney levels in $C(X)$ are not semi-Kelley, answering a question posed by A. Illanes in Problemas propuestos para el taller de Teoría de continuos y sus hiperespacios, Queretaro, 2013