Centers of a dendroid

• Autorzy: Jo Heath , Van C. Nall
• Języki publikacji: EN

Abstrakty

EN

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, every open set intersects uncountably many of these arc components. Moreover, we find that a map from one dendroid to another preserves the center structure if each point inverse has at most countably many components.

Kategorie tematyczne

• 54F15: Continua and generalizations
• 54F50: Spaces of dimension ≤ 1 ; curves, dendrites

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 189
• Numer: 2
• Strony: 173-183

Daty

wydano

2006

Twórcy

autor

Jo Heath

• Mathematics Department, Parker Hall, Auburn University, Auburn, AL 36849-5310, U.S.A.

autor

Van C. Nall

• Department of Mathematics and Computer Science, University of Richmond, Richmond, VA 23173, U.S.A.

Identyfikatory

DOI

10.4064/fm189-2-6