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A continuum whose hyperspace of subcontinua is not its continuous image

Author(s): Alejandro Illanes
Journal: Proc. Amer. Math. Soc. 135 (2007), 4019-4022.
MSC (2000): Primary 54B20
Posted: September 5, 2007
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Abstract: We construct a metric continuum $ X$ such that the hyperspace of subcontinua, $ C(X)$, of $ X$ is not a continuous image of $ X$. This answers a question by I. Krzeminska and J. R. Prajs.

References:

1.
I. Kreminska and J. R. Prajs, On continua whose hyperspace of subcontinua is $ \sigma$-locally connected, Topology Appl. 96 (1999), 53-61. MR 1701239 (2000e:54023)

2.
S. B. Nadler, Jr., Some problems concerning hyperspaces, Topology Conference (V. P. I. and S. U.), Lecture Notes in Math., vol. 375, Springer-Verlag, New York, 1974, Raymond F. Dickman, Jr. and Peter Fletcher, editors, 190-197.MR 0370465 (51:6692)

3.
S. B. Nadler, Jr., Hyperspaces of Sets, Monographs and Textbooks in Pure and Applied Math. Vol. 49, Marcel Dekker, Inc., New York, 1978.MR 0500811 (58:18330)

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Additional Information:

Alejandro Illanes
Affiliation: Instituto de Matematicas, UNAM, Circuito Exterior, Ciudad Universitaria, Mexico, 04510, D.F.
Email: illanes@matem.unam.mx

DOI: 10.1090/S0002-9939-07-08695-9
PII: S 0002-9939(07)08695-9
Keywords: Continuous images, continuum, hyperspaces.
Received by editor(s): April 6, 2005
Received by editor(s) in revised form: March 3, 2006
Posted: September 5, 2007
Communicated by: Alexander N. Dranishnikov
Copyright of article: Copyright 2007, American Mathematical Society

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