On hereditarily indecomposable compacta
L. G. Oversteegen, E. D. Tymchatyn (1986)
Banach Center Publications
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L. G. Oversteegen, E. D. Tymchatyn (1986)
Banach Center Publications
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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.
Wayne Lewis (1983)
Fundamenta Mathematicae
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Lex Oversteegen, E. Tymchatyn (1984)
Fundamenta Mathematicae
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Judy Kennedy (1988)
Colloquium Mathematicae
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Hisao Kato (1991)
Fundamenta Mathematicae
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A. Lelek (1970)
Fundamenta Mathematicae
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Beverly Brechner (1969)
Fundamenta Mathematicae
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T. Maćkowiak (1984)
Fundamenta Mathematicae
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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. ...
Mauricio E. Chacón-Tirado, Alejandro Illanes, Rocío Leonel (2012)
Colloquium Mathematicae
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An embedding from a Cartesian product of two spaces into the Cartesian product of two spaces is said to be factorwise rigid provided that it is the product of embeddings on the individual factors composed with a permutation of the coordinates. We prove that each embedding of a product of two pseudo-arcs into itself is factorwise rigid. As a consequence, if X and Y are metric continua with the property that each of their nondegenerate proper subcontinua is homeomorphic to the pseudo-arc,...