Continua whose hyperspace is a product
Sam Nadler (1980)
Fundamenta Mathematicae
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Sam Nadler (1980)
Fundamenta Mathematicae
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J. Krasinkiewicz, Piotr Minc (1979)
Fundamenta Mathematicae
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Sam Nadler, J. Quinn (1973)
Fundamenta Mathematicae
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E. Tymchatyn (1978)
Fundamenta Mathematicae
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T. Maćkowiak (1976)
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.
Janusz Charatonik (1964)
Fundamenta Mathematicae
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Lex Oversteegen, E. Tymchatyn (1984)
Fundamenta Mathematicae
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J. Roberts, J. Dorroh (1929)
Fundamenta Mathematicae
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Jo Heath, Van C. Nall (2006)
Fundamenta Mathematicae
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A bottleneck in a dendroid is a continuum that intersects every arc connecting two non-empty open sets. Piotr Minc proved that every dendroid contains a point, which we call a center, contained in arbitrarily small bottlenecks. We study the effect that the set of centers in a dendroid has on its structure. We find that the set of centers is arc connected, that a dendroid with only one center has uncountably many arc components in the complement of the center, and that, in this case,...
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...
Charatonik, Janusz J. (2003)
International Journal of Mathematics and Mathematical Sciences
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