Geodesic
Property of being semi-Kelley for the cartesian products and hyperspaces
Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 3, pp. 359-369.

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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.
DOI : 10.14712/1213-7243.2015.217
Classification : 54B20, 54F15, 54G20
Keywords: continuum; property of Kelley; semi-Kelley; cartesian products; hyperspaces; Whitney levels 
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Castañeda-Alvarado, Enrique; Vidal-Escobar, Ivon. Property of being semi-Kelley  for the cartesian products and hyperspaces. Commentationes Mathematicae Universitatis Carolinae, Tome 58 (2017) no. 3, pp. 359-369. doi : 10.14712/1213-7243.2015.217. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.217/

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