Eulerian spaces / Paul Gartside, Max Pitz.

Format:

Book

Author/Creator:

Gartside, Paul (Paul M.), author.

Pitz, Max, author.

Series:

Memoirs of the American Mathematical Society ; v. 1456.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 1456.

Language:

English

Subjects (All):

Topology.

Combinatorial analysis.

Physical Description:

v, 86 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, [2023]

Summary:

"We develop a unified theory of Eulerian spaces by combining the combinatorial theory of infinite, locally finite Eulerian graphs as introduced by Diestel and K¨uhn 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." -- Provided by publisher

Contents:

Introduction

Eulerian maps and Peano graphs

approximating by Eulerian decompositions

product-structured ground spaces

One-dimensional spaces

Notes:

Includes bibliographical references (pages 81-83) and index.

ISBN:

1470467844

9781470467845

OCLC:

1416951621