Arcwise increasing maps

Espinoza, Benjamin; Matsuhashi, Eiichi

doi:10.1016/j.topol.2015.04.010

Cited by 6 publications

(3 citation statements)

References 3 publications

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“…We prove that for each n ≥ 1 the set of all surjective continuumwise injective maps from an n-dimensional continuum onto an LC n−1 -continuum with the disjoint (n−1, n)-cells property is a dense G δ -subset of the space of all surjective maps. This generalizes a result of Espinoza and the second author [5]. …”

supporting

confidence: 90%

Continuum-wise injective maps

Kato

Matsuhashi

2016

Topology and its Applications

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supporting

confidence: 90%

Continuum-wise injective maps

Kato

Matsuhashi

2016

Topology and its Applications

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“…Harrold, in [31], showed that every Peano continuum without free arcs is the strongly irreducible (equivalently, almost injective) image of the circle, and so is Eulerian. We extend this resultand also one of Espinoza & Matsuhashi, see [26] -so as to give more control of the map.…”

Section: 32supporting

confidence: 57%

“…As the results are important for us, and for completeness, we provide brief proofs. For discussions on hereditarily irreducible and arc-wise increasing images of finite graphs see [1,26].…”

Section: Equivalent Definitions For Eulerian Mapsmentioning

confidence: 99%

Eulerian Spaces

Gartside¹,

Pitz²

2019

Preprint

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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 Kühn 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.

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Graph‐like compacta: Characterizations and Eulerian loops

Espinoza

Gartside

Pitz

2020

Journal of Graph Theory

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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 × (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.2010 Mathematics Subject Classification. 05C38, 05C45, 05C63, 54F15, 57M15.

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Arcwise increasing maps

Cited by 6 publications

References 3 publications

Continuum-wise injective maps

Continuum-wise injective maps

Eulerian Spaces

Graph‐like compacta: Characterizations and Eulerian loops

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