| Title:
|
On the hyperspace $C_n(X)/{C_n}_K(X)$ (English) |
| Author:
|
Anaya, José G. |
| Author:
|
Castañeda-Alvarado, Enrique |
| Author:
|
Martínez-Cortez, José A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
62 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
201-224 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a continuum and $n$ a positive integer. Let $C_n(X)$ be the hyperspace of all nonempty closed subsets of $X$ with at most $n$ components, endowed with the Hausdorff metric. For $K$ compact subset of $X$, define the hyperspace ${C_n}_K(X)=\{A\in C_n(X)\colon K\subset A\}$. In this paper, we consider the hyperspace $C_K^n(X)=C_n(X)/{C_n}_K(X)$, which can be a tool to study the space $C_n(X)$. We study this hyperspace in the class of finite graphs and in general, we prove some properties such as: aposyndesis, local connectedness, arcwise disconnectedness, and contractibility. (English) |
| Keyword:
|
hyperspace |
| Keyword:
|
continuum |
| Keyword:
|
containment hyperspace |
| Keyword:
|
aposyndesis |
| Keyword:
|
finite graph |
| Keyword:
|
Peano continuum |
| Keyword:
|
contractibility |
| MSC:
|
54B15 |
| MSC:
|
54B20 |
| MSC:
|
54F15 |
| idZBL:
|
Zbl 07396219 |
| idMR:
|
MR4303578 |
| DOI:
|
10.14712/1213-7243.2021.018 |
| . |
| Date available:
|
2021-07-28T08:38:01Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/149012 |
| . |
| Reference:
|
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