Displaying similar documents to “Exactly two-to-one maps from continua onto some tree-like continua”

Arc property of Kelley and absolute retracts for hereditarily unicoherent continua

Janusz J. Charatonik, Włodzimierz J. Charatonik, Janusz R. Prajs (2003)

Colloquium Mathematicae

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We investigate absolute retracts for hereditarily unicoherent continua, and also the continua that have the arc property of Kelley (i.e., the continua that satisfy both the property of Kelley and the arc approximation property). Among other results we prove that each absolute retract for hereditarily unicoherent continua (for tree-like continua, for λ-dendroids, for dendroids) has the arc property of Kelley.

No arc-connected treelike continuum is the 2-to-1 image of a continuum

Jo Heath, Van C. Nall (2003)

Fundamenta Mathematicae

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In 1940, O. G. Harrold showed that no arc can be the exactly 2-to-1 continuous image of a metric continuum, and in 1947 W. H. Gottschalk showed that no dendrite is a 2-to-1 image. In 2003 we show that no arc-connected treelike continuum is the 2-to-1 image of a continuum.

Whitney properties

J. Krasinkiewicz, Sam Nadler (1978)

Fundamenta Mathematicae

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Exactly two-to-one maps from continua onto arc-continua

Wojciech Dębski, J. Heath, J. Mioduszewski (1996)

Fundamenta Mathematicae

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Continuing studies on 2-to-1 maps onto indecomposable continua having only arcs as proper non-degenerate subcontinua - called here arc-continua - we drop the hypothesis of tree-likeness, and we get some conditions on the arc-continuum image that force any 2-to-1 map to be a local homeomorphism. We show that any 2-to-1 map from a continuum onto a local Cantor bundle Y is either a local homeomorphism or a retraction if Y is orientable, and that it is a local homeomorphism if Y is not orientable. ...