Whitney blocks in the hyperspace of a finite graph
Commentationes Mathematicae Universitatis Carolinae (1995)
- Volume: 36, Issue: 1, page 137-147
- ISSN: 0010-2628
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topIllanes, Alejandro. "Whitney blocks in the hyperspace of a finite graph." Commentationes Mathematicae Universitatis Carolinae 36.1 (1995): 137-147. <http://eudml.org/doc/247751>.
@article{Illanes1995,
abstract = {Let $X$ be a finite graph. Let $C(X)$ be the hyperspace of all nonempty subcontinua of $X$ and let $\mu :C(X)\rightarrow \mathbb \{R\}$ 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 $C(X)$.},
author = {Illanes, Alejandro},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {hyperspaces; Whitney levels; Whitney blocks; finite graphs; finite graph; Whitney map; Whitney levels; Whitney block},
language = {eng},
number = {1},
pages = {137-147},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Whitney blocks in the hyperspace of a finite graph},
url = {http://eudml.org/doc/247751},
volume = {36},
year = {1995},
}
TY - JOUR
AU - Illanes, Alejandro
TI - Whitney blocks in the hyperspace of a finite graph
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 1
SP - 137
EP - 147
AB - Let $X$ be a finite graph. Let $C(X)$ be the hyperspace of all nonempty subcontinua of $X$ and let $\mu :C(X)\rightarrow \mathbb {R}$ 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 $C(X)$.
LA - eng
KW - hyperspaces; Whitney levels; Whitney blocks; finite graphs; finite graph; Whitney map; Whitney levels; Whitney block
UR - http://eudml.org/doc/247751
ER -
References
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