Induced mappings on $C_n(X)/{C_n}_K(X)$

E. Castañeda-Alvarado; J. G. Anaya; J. A. Martínez-Cortez

doi:10.30970/ms.56.1.83-95

E. Castañeda-Alvarado Universidad Autónoma del Estado de México
J. G. Anaya Facultad de ciencias, Universidad Autónoma del Estado de México
J. A. Martínez-Cortez Facultad de ciencias, Universidad Autónoma del Estado de México

DOI: https://doi.org/10.30970/ms.56.1.83-95

Keywords: induced mapping, hyperspaces, continuum, containment hyperspaces, quotient space

Abstract

Given a continuum $X$ and $n\in\mathbb{N}$. Let $C_n(X)$ be the hyperspace of all nonempty closed subsets of $X$ with at most $n$ components. Let ${C_n}_K(X)$ be the hyperspace of all elements in $C_n(X)$ containing $K$ where $K$ is a compact subset of $X$. $C^n_K(X)$ denotes the quotient space $C_n(X)/{C_n}_K(X)$. Given a mapping $f:X\to Y$ between continua, let $C_n(f):C_n(X)\to C_n(Y)$ be the induced mapping by $f$, defined by $C_n(f)(A)=f(A)$. We denote the natural induced mapping between $C^n_K(X)$ and $C^n_{f(K)}(Y)$ by $C^n_K(f)$. In this paper, we study relationships among the mappings $f$, $C_n(f)$ and $C^n_K(f)$ for the following classes of mappings: almost monotone, atriodic, confluent, joining, light, monotone, open, OM, pseudo-confluent, quasi-monotone, semi-confluent, strongly freely decomposable, weakly confluent, and weakly monotone.

Author Biographies

E. Castañeda-Alvarado, Universidad Autónoma del Estado de México

Universidad Autónoma del Estado de México

J. G. Anaya, Facultad de ciencias, Universidad Autónoma del Estado de México

Facultad de ciencias, Universidad Autónoma del Estado de México

J. A. Martínez-Cortez, Facultad de ciencias, Universidad Autónoma del Estado de México

Facultad de ciencias, Universidad Autónoma del Estado de México

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