Eulerian Spaces Steven C. Caton and correlatively on the (good)

and correlatively on the (good) state

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Eulerian Spaces Steven C. Caton and correlatively on the (good)We develop a unified theory of Eulerian spaces by combining the combinatorial theory of infinite, locally finite Eulerian graphs as introduced by Diestel and Kuehn with the topological theory of Eulerian continua defined as irreducible images of the circle, as proposed by Bula, Nikiel and Tymchatyn. First, we clarify the notion of an Eulerian space and establish that all competing definitions in the literature are in fact equivalent. Next, responding