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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Property of Kelley for the Cartesian products and hyperspaces


Authors: Janusz J. Charatonik and Wlodzimierz J. Charatonik
Journal: Proc. Amer. Math. Soc. 136 (2008), 341-346
MSC (2000): Primary 54B10, 54B20, 54F15
Published electronically: September 25, 2007
MathSciNet review: 2350421
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Abstract: A continuum $ X$ having the property of Kelley is constructed such that neither $ X \times [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.


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Additional Information

Janusz J. Charatonik
Affiliation: Mathematical Institute, University of Wrocław, Wrocław, Poland; and Instituto de Matemàticas, UNAM, Cuidad Universitaria, Mexico

Wlodzimierz J. Charatonik
Affiliation: Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, Missouri 65409-0020
Email: wjcharat@umr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08650-9
PII: S 0002-9939(07)08650-9
Keywords: Cartesian product, continuum, hyperspace, property of Kelley
Received by editor(s): July 9, 2004
Received by editor(s) in revised form: January 15, 2006
Published electronically: September 25, 2007
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.