Homotopically fixed arcs and the contractibility of dendroids
Janusz Charatonik, Z. Grabowski (1978)
Fundamenta Mathematicae
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Homotopically fixed arcs and the contractibility of dendroids
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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,...
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