Induced mappings on $C_n(X)/{C_n}_K(X)$
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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | deu |
| Published: |
Ivan Franko National University of Lviv
2021-10-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/101 |
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| Summary: | 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. |
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| ISSN: | 1027-4634 2411-0620 |