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Property of Kelley for the Cartesian products and hyperspaces

Author(s): Janusz J. Charatonik; Wlodzimierz J. Charatonik
Journal: Proc. Amer. Math. Soc. 136 (2008), 341-346.
MSC (2000): Primary 54B10, 54B20, 54F15
Posted: September 25, 2007
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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.

References:

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J. J. Charatonik and W. J. Charatonik, Weak and small Whitney properties, Topology Proc. 28 (2004), 69-79. MR 2105448 (2005g:54018)

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W. J. Charatonik, Hyperspaces and the property of Kelley, Bull. Polish Acad. Sci. Math. 30 (1982), 457-459. MR 0703573 (85c:54052)

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W. J. Charatonik, A homogeneous continuum without the property of Kelley, Topology Appl. 96 (1999), 209-216. MR 1709689 (2000i:54044)

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H. Kato, On the property of Kelley in the hyperspace and Whitney continua, Topology Appl. 30 (1988), 165-174. MR 0967753 (90b:54006)

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H. Kato, A note on continuous mappings and the property of J. L. Kelley, Proc. Amer. Math. Soc. 112 (1991), 1143-1148. MR 1073527 (91j:54013)

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J. L. Kelley, Hyperspaces of a continuum, Trans. Amer. Math. Soc. 52 (1942), 22-36. MR 0006505 (3:315b)

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S. B. Nadler, Jr., Hyperspaces of sets, M. Dekker, New York and Basel, 1978.MR 0500811 (58:18330)

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R. W. Wardle, On a property of J. L. Kelley, Houston J. Math. 3 (1977), 291-299.MR 0458379 (56:16582)

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Additional Information:

Janusz J. Charatonik
Affiliation: Mathematical Institute, University of Wroclaw, Wroclaw, 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: 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
Posted: September 25, 2007
Communicated by: Alexander N. Dranishnikov
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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