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Graph-like compacta: Characterizations and Eulerian loops

Authors:	Benjamin Espinoza Paul Gartside Max Pitz

Institution:	1. Department of Mathematics, University of Pittsburgh at Greensburg, Greensburg, Pennsylvania;2. Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania;3. Department of Mathematics, University of Hamburg, Hamburg, Germany

Abstract:	A compact graph-like space is a triple $(X, V, E)$ , where $X$ is a compact, metrizable space, $V ? X$ is a closed zero-dimensional subset, and $E$ is an index set such that $X ? V ? ?+? E \times (0, 1)$ . 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.

Keywords:	end Eulerian Freudenthal compactification graph-like space infinite graph locally finite graph topology