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9781470467845 Academic Inspection Copy

Eulerian Spaces

  • ISBN-13: 9781470467845
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Paul Gartside, By Max Pitz
  • Price: AUD $219.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 29/05/2024
  • Format: Paperback (254.00mm X 178.00mm) 86 pages Weight: 272g
  • Categories: Geometry [PBM]Topology [PBP]
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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 to an unsolved problem of Treybig and Ward from 1981, we formulate a combinatorial conjecture for characterising the Eulerian spaces, in a manner that naturally extends the characterisation for finite Eulerian graphs. Finally, we present far-reaching results in support of our conjecture which together subsume and extend all known results about the Eulerianity of infinite graphs and continua to date. In particular, we characterise all one-dimensional Eulerian spaces.
Paul Gartside, University of Pittsburgh, Pennsylvania. Max Pitz, Universitat Hamburg, Germany.
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