Induced mappings on hyperspaces $F_n^K\left(X\right)$

Castañeda-Alvarado, Enrique, Mondragón-Alvarez, Roberto C., and Ordoñez, Norberto. "Induced mappings on hyperspaces $F_n^K(X)$." Commentationes Mathematicae Universitatis Carolinae (2024): 79-97. <http://eudml.org/doc/299940>.

@article{Castañeda2024,
abstract = {Given a metric continuum $X$ and a positive integer $n$, $F_\{n\}(X)$ denotes the hyperspace of all nonempty subsets of $X$ with at most $n$ points endowed with the Hausdorff metric. For $K\in F_\{n\}(X)$, $F_\{n\}(K,X)$ denotes the set of elements of $F_\{n\}(X)$ containing $K$ and $F_\{n\}^K(X)$ denotes the quotient space obtained from $F_\{n\}(X)$ by shrinking $F_\{n\}(K,X)$ to one point set. Given a map $f\colon X\rightarrow Y$ between continua, $f_\{n\}\colon F_\{n\}(X)\rightarrow F_\{n\}(Y)$ denotes the induced map defined by $f_\{n\}(A)=f(A)$. Let $K\in F_\{n\}(X)$, we shall consider the induced map in the natural way $f_\{n,K\}\colon F_\{n\}^K(X)\rightarrow F_\{n\}^\{f(K)\}(Y)$. In this paper we consider the maps $f$, $f_\{n\}$, $f_\{n,K\}$ for some $K\in F_n(X)$ and $f_\{n,K\}$ for each $K\in F_n(X)$; and we study relationship between them for the following classes of maps: homeomorphisms, monotone, confluent, light and open maps.},
author = {Castañeda-Alvarado, Enrique, Mondragón-Alvarez, Roberto C., Ordoñez, Norberto},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {continuum; symmetric product; quotient space; hyperspace; induced mapping},
language = {eng},
number = {1},
pages = {79-97},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Induced mappings on hyperspaces $F_n^K(X)$},
url = {http://eudml.org/doc/299940},
year = {2024},
}

TY - JOUR
AU - Castañeda-Alvarado, Enrique
AU - Mondragón-Alvarez, Roberto C.
AU - Ordoñez, Norberto
TI - Induced mappings on hyperspaces $F_n^K(X)$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2024
PB - Charles University in Prague, Faculty of Mathematics and Physics
IS - 1
SP - 79
EP - 97
AB - Given a metric continuum $X$ and a positive integer $n$, $F_{n}(X)$ denotes the hyperspace of all nonempty subsets of $X$ with at most $n$ points endowed with the Hausdorff metric. For $K\in F_{n}(X)$, $F_{n}(K,X)$ denotes the set of elements of $F_{n}(X)$ containing $K$ and $F_{n}^K(X)$ denotes the quotient space obtained from $F_{n}(X)$ by shrinking $F_{n}(K,X)$ to one point set. Given a map $f\colon X\rightarrow Y$ between continua, $f_{n}\colon F_{n}(X)\rightarrow F_{n}(Y)$ denotes the induced map defined by $f_{n}(A)=f(A)$. Let $K\in F_{n}(X)$, we shall consider the induced map in the natural way $f_{n,K}\colon F_{n}^K(X)\rightarrow F_{n}^{f(K)}(Y)$. In this paper we consider the maps $f$, $f_{n}$, $f_{n,K}$ for some $K\in F_n(X)$ and $f_{n,K}$ for each $K\in F_n(X)$; and we study relationship between them for the following classes of maps: homeomorphisms, monotone, confluent, light and open maps.
LA - eng
KW - continuum; symmetric product; quotient space; hyperspace; induced mapping
UR - http://eudml.org/doc/299940
ER -