| Title:
|
Continua with unique symmetric product (English) |
| Author:
|
Anaya, José G. |
| Author:
|
Castañeda-Alvarado, Enrique |
| Author:
|
Illanes, Alejandro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
54 |
| Issue:
|
3 |
| Year:
|
2013 |
| Pages:
|
397-406 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a metric continuum. Let $F_{n}(X)$ denote the hyperspace of nonempty subsets of $X$ with at most $n$ elements. We say that the continuum $X$ has unique hyperspace $F_{n}(X)$ provided that the following implication holds: if $Y$ is a continuum and $F_{n}(X)$ is homeomorphic to $F_{n}(Y)$, then $X$ is homeomorphic to $Y$. In this paper we prove the following results: (1) if $X$ is an indecomposable continuum such that each nondegenerate proper subcontinuum of $X$ is an arc, then $X$ has unique hyperspace $F_{2}(X)$, and (2) let $X$ be an arcwise connected continuum for which there exists a unique point $v\in X$ such that $v$ is the vertex of a simple triod. Then $X$ has unique hyperspace $F_{2}(X)$. (English) |
| Keyword:
|
arc continuum |
| Keyword:
|
continuum |
| Keyword:
|
indecomposable |
| Keyword:
|
symmetric product |
| Keyword:
|
unique hyperspace |
| MSC:
|
54B20 |
| MSC:
|
54F15 |
| . |
| Date available:
|
2013-06-29T06:56:22Z |
| Last updated:
|
2015-10-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143309 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| . |
