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Displaying similar documents to “Planable and smooth dendroids”

Centers of a dendroid

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,...

On smooth dendroids

Janusz Charatonik, Carl Eberhart (1970)

Fundamenta Mathematicae

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A fixed-point anomaly in the plane

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.