Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 38 No. 2 (2020): Revista integración, temas de matemáticas
Research and Innovation Articles

A characterization of inducible mappings between hyperspaces

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  • José G. Anaya,
  • David Maya,
  • Fernando Orozco Zitli
José G. Anaya
Universidad Autónoma del Estado de México
David Maya
Universidad Autónoma del Estado de México
Fernando Orozco Zitli
Universidad Autónoma del Estado de México
DOI: https://doi.org/10.18273/revint.v38n2-2020004

Published 2020-11-20

Keywords

  • Continuum,
  • hyperspace,
  • induced mapping,
  • inducible mapping

How to Cite

Anaya, J. G., Maya, D., & Zitli, F. O. (2020). A characterization of inducible mappings between hyperspaces. Revista Integración, Temas De matemáticas, 38(2), 109–117. https://doi.org/10.18273/revint.v38n2-2020004

Copyright (c) 2020 Revista Integración, temas de matemáticas

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

For fixed hyperspaces H(X) and H(Y ) of metric continua X and Y , respectively, a mapping g : H(X) → H(Y ) is called inducible provided that there exists a mapping f : X → Y such that g(A) = {f(a) : a ∈ A}, for every A ∈ H(X). In this paper, we present a characterization of inducible mappings between hyperspaces, compare it with the necessary and sufficient conditions under which a mapping between hyperspaces g is inducible given by J.J. Charatonik and W.J. Charatonik in 1998, and exhibit examples to show the independence among the conditions in both characterizations in all hyperespaces, some of them have not been considered in the known characterization, doing complete the study of this class of mappings.

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References

Charatonik J.J., “Recent research in hyperspace theory”, Extracta Math. 18 (2003), No. 2, 235-262.

Charatonik J.J. and Charatonik W.J., “Inducible mappings between hyperspaces”, Bull. Pol. Acad. Sci. Math. 46 (1998), No. 1, 5-9.

Charatonik J.J., Illanes A. and Macías S., “Induced mapping on the hyperspaces Cn(X) of a continuum X”, Houston J. Math. 28 (2002), No. 4, 781-805.

Illanes A. and Nadler, S.B.Jr., Hyperspaces: Fundamentals and recent advances, Monographs and Textbooks in Pure and Applied Math., Vol. 216, Marcel Dekker, Inc., New York, 1999.

Michael E., “Topologies on spaces of subsets”, Trans. Amer. Math. Soc. 71 (1951), 152-182. doi: 10.1090/s0002-9947-1951-0042109-4