Given a metric continumm X, let $CB(X)$ be the hyperspace of subcontinua of X with connected boundary. In this paper we present results concerning $CB(X)$, first about continua for which every subcontinuum has connected boundary. Then we study continua that only have one-point sets as connected boundary proper subcontinua. Later we include characterizations of arcs and simple closed curves. Finally we give a formula for the number of components of $CB(X)$ for finite graphs.

中文翻译：

---

连续统一体的连通边界子连续群的超空间

给定度量连续毫米X，令$C乙（X）$是具有连接边界的X子连续体的超空间。在本文中，我们提出了有关$C乙（X）$，首先是关于每个子连续体都有连接边界的连续体。然后，我们研究仅具有一个点集作为连接边界固有子连续体的连续体。稍后，我们将描述圆弧和简单闭合曲线的特征。最后，我们给出一个公式来计算$C乙（X）$ 用于有限图。