Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4661238 | Topology and its Applications | 2007 | 6 Pages |
Abstract
A bottleneck in a dendroid is a continuum that intersects every arc connecting two nonempty open sets. Every dendroid contains a point called a center which is contained in arbitrarily small bottlenecks. A subset A of a dendroid is a shore set if for every ε>0 there is a continuum in D∖A with Hausdorff distance from D less than ε. If a shore set has only one point it is called a shore point. This paper explores the relationship between center points and shore points in a dendroid. We show that if a dendroid contains a strong center, then any finite union of the arc components of the set of shore points is a shore set.
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Physical Sciences and Engineering
Mathematics
Geometry and Topology