Graph-Like Compacta: Characterizations and Eulerian Loops

Abstract

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.

27 pages; coloured fugures