Hyperspaces of arcs containing a point - Chacón-Tirado, Mauricio; López, María de J.; Suárez-López, José Luis (Topology Proceedings, 2023)
For a metric continuum $X$ and for $p \in X$, we define the hyperspace $\operatorname{Arcs}(p, X)$ as the set of all arcs in $X$ that contain the point $p$, endowed with the Hausdorff metric. We show geometric models of $\operatorname{Arcs}(p, X)$, in the case when $X$ is the arc, the simple closed curve, the simple triod, the noose and the $\sin \left(\frac{1}{x}\right)$-continuum. Moreover, we present a characterization of dendrites in terms of this hyperspace.