The hyperspace of non-cut subcontinua of graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916811974377472 |
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| author | Illanes, Alejandro Martínez-de-la-Vega, Verónica Vega, Jorge E. |
| author_facet | Illanes, Alejandro Martínez-de-la-Vega, Verónica Vega, Jorge E. |
| contents | Given a continuum $X$, let $C(X)$ be the hyperspace of all subcontinua of $X$. We consider the hyperspace $NC^{*}(X)=\{A\in C(X):X\setminus A$ is connected$\}$. In this paper we prove that the only locally connected continua $X$ for which $NC^{*}(X)$ is compact are the arcs and the simple closed curves. We also characterize the finite graphs $G$ for which $NC^{*}(G)$ is connected. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The hyperspace of non-cut subcontinua of graphs Illanes, Alejandro Martínez-de-la-Vega, Verónica Vega, Jorge E. General Topology Primary 54F16, Secondary 54F15, 54F50, 54F65 Given a continuum $X$, let $C(X)$ be the hyperspace of all subcontinua of $X$. We consider the hyperspace $NC^{*}(X)=\{A\in C(X):X\setminus A$ is connected$\}$. In this paper we prove that the only locally connected continua $X$ for which $NC^{*}(X)$ is compact are the arcs and the simple closed curves. We also characterize the finite graphs $G$ for which $NC^{*}(G)$ is connected. |
| title | The hyperspace of non-cut subcontinua of graphs |
| topic | General Topology Primary 54F16, Secondary 54F15, 54F50, 54F65 |
| url | https://arxiv.org/abs/2503.18196 |