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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Ivan Franko National University of Lviv
2021-10-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/101 |
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| author | E. Castañeda-Alvarado J. G. Anaya J. A. Martínez-Cortez |
| author_facet | E. Castañeda-Alvarado J. G. Anaya J. A. Martínez-Cortez |
| author_sort | E. Castañeda-Alvarado |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-25c9faa3b9c243d19c3b9901e1a518e5 |
| institution | Matheson Library |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2021-10-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-25c9faa3b9c243d19c3b9901e1a518e52025-07-08T09:14:29ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202021-10-01561839510.30970/ms.56.1.83-95101Induced mappings on $C_n(X)/{C_n}_K(X)$E. Castañeda-Alvarado0J. G. Anaya1J. A. Martínez-Cortez2Universidad Autónoma del Estado de MéxicoFacultad de ciencias, Universidad Autónoma del Estado de MéxicoFacultad de ciencias, Universidad Autónoma del Estado de MéxicoGiven 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.http://matstud.org.ua/ojs/index.php/matstud/article/view/101induced mappinghyperspacescontinuumcontainment hyperspacesquotient space |
| spellingShingle | E. Castañeda-Alvarado J. G. Anaya J. A. Martínez-Cortez Induced mappings on $C_n(X)/{C_n}_K(X)$ Математичні Студії induced mapping hyperspaces continuum containment hyperspaces quotient space |
| title | Induced mappings on $C_n(X)/{C_n}_K(X)$ |
| title_full | Induced mappings on $C_n(X)/{C_n}_K(X)$ |
| title_fullStr | Induced mappings on $C_n(X)/{C_n}_K(X)$ |
| title_full_unstemmed | Induced mappings on $C_n(X)/{C_n}_K(X)$ |
| title_short | Induced mappings on $C_n(X)/{C_n}_K(X)$ |
| title_sort | induced mappings on c n x c n k x |
| topic | induced mapping hyperspaces continuum containment hyperspaces quotient space |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/101 |
| work_keys_str_mv | AT ecastanedaalvarado inducedmappingsoncnxcnkx AT jganaya inducedmappingsoncnxcnkx AT jamartinezcortez inducedmappingsoncnxcnkx |