arXiv subjects
Publications and source records attributed to Jorge E. Vega.
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.
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.