Author:
Castañeda-Alvarado E.,Anaya J. G.,Martínez-Cortez J. A.
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.
Publisher
Ivan Franko National University of Lviv
Reference33 articles.
1. J.G. Anaya, F. Capul´ın, M.A. Lara, F. Orozco-Zitli, Induced mappings between quotient spaces of n-fold hyperspaces of continua, Glas. Mat., III. Ser., 51 (2016), №2, 475–490. doi:10.3336/gm.51.2.13
2. J.G. Anaya, E. Casta˜neda-Alvarado, J.A. Mart´ınez-Cortez, On the hyperspace Cn(X)/CnK(X), accepted for publication in Comment. Math. Univ. Carolin.
3. F. Barrag´an, Induced maps on n-fold symmetric product suspensions, Topology Appl., 158 (2011), №10, 1192–1205. doi.org/10.1016/j.topol.2011.04.006
4. F. Barrag´an, S. Mac´ıas, J.F. Tenorio, More on induced maps on n-fold symmetric product suspensions Glas. Mat., III. Ser., 50 (2015), №2, 489–512. doi:10.3336/gm.50.2.15
5. J. Camargo, Openness of the induced map Cn(f), Bol. Mat. (N.S.), 16 (2009), №2, 115–123. https://revistas.unal.edu.co/index.php/bolma/article/view/40781