Abstract

G. ANAY, José; MAYA, David  and  OROZCO-ZITL, Fernando. A characterization of inducible mappings between hyperspaces. Integración - UIS [online]. 2020, vol.38, n.2, pp.109-117.  Epub June 30, 2020. ISSN 0120-419X.  https://doi.org/10.18273/revint.v38n2-2020004.

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.

Keywords : Continuum; hyperspace; induced mapping; inducible mapping.

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