| Title:
|
Whitney blocks in the hyperspace of a finite graph (English) |
| Author:
|
Illanes, Alejandro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
36 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
137-147 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $X$ be a finite graph. Let $C(X)$ be the hyperspace of all nonempty subcontinua of $X$ and let $\mu :C(X)\rightarrow \Bbb R$ be a Whitney map. We prove that there exist numbers $0<T_0<T_1<T_2<\dots <T_M=\mu (X)$ such that if $T\in (T_{i-1},T_i)$, then the Whitney block $\mu ^{-1} (T_{i-1},T_i)$ is homeomorphic to the product $\mu ^{-1}(T)\times (T_{i-1},T_i)$. We also show that there exists only a finite number of topologically different Whitney levels for $C(X)$. (English) |
| Keyword:
|
hyperspaces |
| Keyword:
|
Whitney levels |
| Keyword:
|
Whitney blocks |
| Keyword:
|
finite graphs |
| MSC:
|
05C10 |
| MSC:
|
52B99 |
| MSC:
|
54B20 |
| idZBL:
|
Zbl 0833.54009 |
| idMR:
|
MR1334422 |
| . |
| Date available:
|
2009-01-08T18:16:39Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118740 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Duda R.: Correction to the paper ``On the hyperspace of subcontinua of a finite graph I.Fund. Math. 69 (1970), 207-211. MR 0273575 |
| 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:
|
[10] Puga-Espinosa I.: Hiperespacios con punta de cono.Tesis doctoral, Facultad de Ciencias, Universidad Nacional Autónoma de México, 1989. |
| . |
