A continuum whose hyperspace of subcontinua is not its continuous image
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- by Alejandro Illanes PDF
- Proc. Amer. Math. Soc. 135 (2007), 4019-4022 Request permission
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. Krzemińska and J. R. Prajs.References
- Iwona Krzemińska and Janusz R. Prajs, On continua whose hyperspace of subcontinua is $\sigma$-locally connected, Topology Appl. 96 (1999), no. 1, 53–61. MR 1701239, DOI 10.1016/S0166-8641(98)00014-5
- Sam B. Nadler Jr., Some problems concerning hyperspaces, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973) Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974, pp. 190–197. MR 0370465
- Sam B. Nadler Jr., Hyperspaces of sets, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 49, Marcel Dekker, Inc., New York-Basel, 1978. A text with research questions. MR 0500811
Additional Information
- Alejandro Illanes
- Affiliation: Instituto de Matematicas, UNAM, Circuito Exterior, Ciudad Universitaria, Mexico, 04510, D.F.
- Email: illanes@matem.unam.mx
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 4019-4022
- MSC (2000): Primary 54B20
- DOI: https://doi.org/10.1090/S0002-9939-07-08695-9
- MathSciNet review: 2341953