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arXiv · 2503.18196

The hyperspace of non-cut subcontinua of graphs

Alejandro Illanes·Verónica Martínez-de-la-Vega·Jorge E. Vega
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Abstract

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.

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Alejandro Illanes, Verónica Martínez-de-la-Vega, Jorge E. Vega. 2025-03-23. The hyperspace of non-cut subcontinua of graphs. https://arxiv.org/abs/2503.18196

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