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Theorems of Maclane and Whitney for Graph-Like Spaces

The planarity theorems of MacLane and Whitney are extended to compact graph–like spaces. This generalizes recent results of Bruhn and Stein (MacLane’s Theorem for the Freudenthal compactification of a locally finite graph) and of Bruhn and Diestel (Whitney’s Theorem for an identification space obtained from a graph in which no two vertices are joined by infinitely many edge-disjoint paths).