Centers and shore sets of a dendroid
by
Van Nall
University of Richmond

A point p in a dendroid D is a center for D if there are two points b and c in D such that for every e > 0 there is a continuum C containing p of diameter less than e, and there are open sets U and V containing b and c respectively such that every arc from U to V intersects C. A subset A of a dendroid is a shore set if for every e > 0 there is a continuum in D \A with Hausdorff distance from D less than e. We explore the relationship between centers and shore sets and prove some theorems about when the union of shore sets is a shore set.

Date received: February 28, 2006