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.
Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.