Article
| Title: | Induced mappings on hyperspaces $F_n^K(X)$ (English) |
| Author: | Castañeda-Alvarado, Enrique |
| Author: | Mondragón-Alvarez, Roberto C. |
| Author: | Ordoñez, Norberto |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 65 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 79-97 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | 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 $f\colon X\to Y$ between continua, $f_{n}\colon F_{n}(X)\to F_{n}(Y)$ denotes the induced map defined by $f_{n}(A)=\nobreak f(A)$. Let $K\in F_{n}(X)$, we shall consider the induced map in the natural way $f_{n,K}\colon F_{n}^K(X)\to F_{n}^{f(K)}(Y)$. 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. (English) |
| Keyword: | continuum |
| Keyword: | symmetric product |
| Keyword: | quotient space |
| Keyword: | hyperspace |
| Keyword: | induced mapping |
| MSC: | 54B15 |
| MSC: | 54B20 |
| MSC: | 54C05 |
| MSC: | 54C10 |
| DOI: | 10.14712/1213-7243.2024.016 |
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| Date available: | 2025-04-24T07:51:26Z |
| Last updated: | 2025-04-25 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152946 |
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