A collection of dendroids.
Charatonik, Janusz J., Charatonik, Włodzimierz J. (2000)
Mathematica Pannonica
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Charatonik, Janusz J., Charatonik, Włodzimierz J. (2000)
Mathematica Pannonica
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T. Maćkowiak (1976)
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,...
Janusz Charatonik, Z. Grabowski (1978)
Fundamenta Mathematicae
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J. Chartonik (1980)
Fundamenta Mathematicae
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Sam Nadler, J. Quinn (1973)
Fundamenta Mathematicae
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Janusz Charatonik, Carl Eberhart (1970)
Fundamenta Mathematicae
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A. Lelek (1961)
Fundamenta Mathematicae
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Charles L. Hagopian, Janusz R. Prajs (2005)
Fundamenta Mathematicae
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We define an unusual continuum M with the fixed-point property in the plane ℝ². There is a disk D in ℝ² such that M ∩ D is an arc and M ∪ D does not have the fixed-point property. This example answers a question of R. H. Bing. The continuum M is a countable union of arcs.
Charatonik, Janusz J., Illanes, Alejandro (2004)
International Journal of Mathematics and Mathematical Sciences
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