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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 $g$-contractible


Author: Alejandro Illanes
Journal: Proc. Amer. Math. Soc. 130 (2002), 2179-2182
MSC (2000): Primary 54B20
Published electronically: February 12, 2002
MathSciNet review: 1896056
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Abstract: A topological space $Y$ is said to be $g$-contractible provided that there exists a continuous onto function $f:Y\rightarrow Y$ such that $f$ is homotopic to a constant function. Answering a question by Sam B. Nadler, Jr., in this paper we construct a metric continuum $Z$ such that its hyperspace of subcontinua $C(Z)$ is not $g$-contractible.


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Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06307-4
PII: S 0002-9939(02)06307-4
Keywords: Continuum, $g$-contractible, hyperspace
Received by editor(s): April 24, 2000
Received by editor(s) in revised form: February 19, 2001
Published electronically: February 12, 2002
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society