The hyperspace of non-cut subcontinua of graphs and dendrites
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909061781389312 |
|---|---|
| author | Hernández-Gutiérrez, Rodrigo Martínez-de-la-Vega, Verónica Martínez-Montejano, Jorge M. Vega, Jorge E. |
| author_facet | Hernández-Gutiérrez, Rodrigo Martínez-de-la-Vega, Verónica Martínez-Montejano, Jorge M. Vega, Jorge E. |
| contents | Given a continuum $X$, let $C(X)$ denote the hyperspace of all subcontinua of $X$. In this paper we study the Vietoris hyperspace $NC^{*}(X)=\{ A \in C(X):X\setminus A\text{ is connected}\}$ when $X$ is a finite graph or a dendrite; in particular, we give conditions under which $NC^{*}(X)$ is compact, connected, locally connected or totally disconnected. Also, we prove that if $X$ is a dendrite and the set of endpoints of $X$ is dense, then $NC^{*}(X)$ is homeomorphic to the Baire space of irrational numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_06020 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The hyperspace of non-cut subcontinua of graphs and dendrites Hernández-Gutiérrez, Rodrigo Martínez-de-la-Vega, Verónica Martínez-Montejano, Jorge M. Vega, Jorge E. General Topology 54F50, 54B20, 54E50, 54F15, 54F65 Given a continuum $X$, let $C(X)$ denote the hyperspace of all subcontinua of $X$. In this paper we study the Vietoris hyperspace $NC^{*}(X)=\{ A \in C(X):X\setminus A\text{ is connected}\}$ when $X$ is a finite graph or a dendrite; in particular, we give conditions under which $NC^{*}(X)$ is compact, connected, locally connected or totally disconnected. Also, we prove that if $X$ is a dendrite and the set of endpoints of $X$ is dense, then $NC^{*}(X)$ is homeomorphic to the Baire space of irrational numbers. |
| title | The hyperspace of non-cut subcontinua of graphs and dendrites |
| topic | General Topology 54F50, 54B20, 54E50, 54F15, 54F65 |
| url | https://arxiv.org/abs/2108.06020 |