Induced and inducible mappings between hyperspaces - Fuentes-Montes de Oca, Alejandro (2019)
In this paper we consider H(X) be a hyperspace of a continuum X. Let f : X → Y be a continuous function between continua, consider the induced function H(f) : H(X) → H(Y ) given by H(f)(A) = f(A), for all A ϵ H(X). On the other hand, if we have the continuous function H : H(X) → H(Y ) and there exists g : X → Y such that H = H(f), we say that H is inducible. Three classes of functions between continua are presented and the following problem is studied: f belongs to a class if and only if the induced function H(f) also belongs to that class. In addition, a characterization for the inducible functions is presented and with this of sample an application to order embedding.