A compact graph-like space is a triple $(X,V,E)$ where $X$ is a compact, metrizable space, $V \subseteq X$ is a closed zero-dimensional subset, and $E$ is an index set such that $X \setminus V \cong E \times (0,1)$. New characterizations of compact graph-like spaces are given, connecting them to certain classes of continua, and to standard subspaces of Freudenthal compactifications of locally finite graphs. These are applied to characterize Eulerian graph-like compacta.

中文翻译：

---

类图压缩：特征和欧拉环

一个紧凑的类图空间是一个三元组 $(X,V,E)$，其中 $X$ 是一个紧凑的、可度量的空间，$V \subseteq X$ 是一个封闭的零维子集，而 $E$ 是一个索引设置使得 $X \setminus V \cong E \times (0,1)$。给出了致密类图空间的新特征，将它们连接到某些连续体类，以及局部有限图的 Freudenthal 紧化的标准子空间。这些被应用于表征欧拉图状致密体。