Planable and smooth dendroids
Mackowiak, T.
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Mackowiak, T.
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T. Maćkowiak (1976)
Fundamenta Mathematicae
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J. Krasinkiewicz, Piotr Minc (1979)
Fundamenta Mathematicae
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Janusz Charatonik, Z. Grabowski (1978)
Fundamenta Mathematicae
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Sam Nadler, J. Quinn (1973)
Fundamenta Mathematicae
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Charatonik, Janusz J., Charatonik, Włodzimierz J. (2000)
Mathematica Pannonica
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Sam Nadler (1980)
Fundamenta Mathematicae
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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.
Charatonik, Janusz J. (2003)
International Journal of Mathematics and Mathematical Sciences
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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...