Abstract: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 {\it A weaker form of the property of Kelley\/}, Topology Proc. {\bf 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 {\it Problemas propuestos para el taller de Teor\'ia de continuos y sus hiperespacios\/}, Queretaro, 2013.
Keywords: continuum; property of Kelley; semi-Kelley; cartesian products; hyperspaces; Whitney levels
DOI: DOI 10.14712/1213-7243.2015.217
AMS Subject Classification: 54F15 54B20 54G20