| 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 |
| . |
| Category:
|
math |
| . |
| 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 |
| idZBL:
|
Zbl 08063788 |
| idMR:
|
MR4899032 |
| DOI:
|
10.14712/1213-7243.2024.016 |
| . |
| Date available:
|
2025-04-24T07:51:26Z |
| Last updated:
|
2026-07-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152946 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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