Induced and inducible mappings between hyperspaces
DOI:
https://doi.org/10.15381/pes.v21i2.15722Keywords:
Continuum, hyperspace, induced function, inducible function and order embeddingAbstract
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.
Downloads
Published
Issue
Section
License
Copyright (c) 2019 Alejandro Fuentes-Montes de Oca
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
THE AUTHORS RETAIN THEIR RIGHTS:
a) The authors retain their trademark and patent rights, and also on any process or procedure described in the article.
b) The authors retain the right to share, copy, distribute, execute and publicly communicate the article published in Pesquimat magazine (for example, place it in an institutional repository or publish it in a book), with recognition of its initial publication in the Pesquimat magazine.
c) The authors retain the right to make a later publication of their work, to use the article or any part of it (for example: a compilation of their works, notes for conferences, thesis, or for a book), provided that they indicate the source of publication (authors of the work, magazine, volume, number and date).
