A continuum X having the property of Kelley is constructed such that neither X × [0, 1], nor the hyperspace C(X), nor small Whitney levels in C(X) have the property of Kelley. This answers several questions asked in the literature.
W. J. Charatonik and J. J. Charatonik, "Property of Kelley for the Cartesian Products and Hyperspaces," Proceedings of the American Mathematical Society, vol. 136, no. 1, pp. 341-346, American Mathematical Society, Jan 2008.
The definitive version is available at http://dx.doi.org/10.1090/S0002-9939-07-08650-9
Mathematics and Statistics
Keywords and Phrases
Cartesian Product; Continuum; Property Of Kelley; Continuity; Hyperspace
Article - Journal
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