Decomposable circle-like continua
W.T. Ingram (1968)
Fundamenta Mathematicae
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Displaying similar documents to “Solenoids and inverse limits of sequences of arcs with open bonding maps”
Decomposable circle-like continua
A hereditarily indecomposable, hereditarily non-chainable planar tree-like continuum
Lee Mohler, Lex Oversteegen (1984)
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Kazuhiro Kawamura (1991)
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On span and chainable continua
Lex Oversteegen, E. Tymchatyn (1984)
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An atriodic tree-like continuum with positive span which admits a monotone mapping to a chainable continuum
James Davis, W. Ingram (1988)
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Whitney properties
J. Krasinkiewicz, Sam Nadler (1978)
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William Mahavier (1967)
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Exactly two-to-one maps from continua onto some tree-like continua
Wojciech Dębski, J. Heath, J. Mioduszewski (1992)
Fundamenta Mathematicae
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It is known that no dendrite (Gottschalk 1947) and no hereditarily indecomposable tree-like continuum (J. Heath 1991) can be the image of a continuum under an exactly 2-to-1 (continuous) map. This paper enlarges the class of tree-like continua satisfying this property, namely to include those tree-like continua whose nondegenerate proper subcontinua are arcs. This includes all Knaster continua and Ingram continua. The conjecture that all tree-like continua have this property, stated...
Continua which admit no mean
K. Kawamura, E. Tymchatyn (1996)
Colloquium Mathematicae
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A symmetric, idempotent, continuous binary operation on a space is called a mean. In this paper, we provide a criterion for the non-existence of mean on a certain class of continua which includes tree-like continua. This generalizes a result of Bell and Watson. We also prove that any hereditarily indecomposable circle-like continuum admits no mean.
On finitely equivalent continua.
Charatonik, Janusz J. (2003)
International Journal of Mathematics and Mathematical Sciences
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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. ...