Hyperspaces $C(p,X)$ of finite graphs
| Autor: | Corona-Vázquez, Florencio, Estrella, Russell Aarón Quiñones, Sánchez-Martínez, Javier, Villanueva, Hugo |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Topology and its Apllications 2018 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.topol.2018.08.007 |
| Popis: | Given a continuum $X$ and $p\in X$, we will consider the hyperspace $C(p,X)$ of all subcontinua of $X$ containing $p$ and the family $K(X)$ of all hyperspaces $C(q,X)$, where $q\in X$. In this paper we give some conditions on the points $p,q\in X$ to guarantee that $C(p,X)$ and $C(q,X)$ are homeomorphic, for finite graphs $X$. Also, we study the relationship between the homogeneity degree of a finite graph $X$ and the number of topologically distinct spaces in $K(X)$, called the size of $K(X)$. In addition, we construct for each positive integer $n$, a finite graph $X_n$ such that $K(X_n)$ has size $n$, and we present a theorem that allows to construct finite graphs $X$ with a degree of homogeneity different from the size of the family $K(X)$. Comment: 16 pages |
| Databáze: | arXiv |
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