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

 

A continuum whose hyperspace of subcontinua is not its continuous image


Author: Alejandro Illanes
Journal: Proc. Amer. Math. Soc. 135 (2007), 4019-4022
MSC (2000): Primary 54B20
Published electronically: September 5, 2007
MathSciNet review: 2341953
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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.


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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: http://dx.doi.org/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
Published electronically: September 5, 2007
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2007 American Mathematical Society