Abstrakt
A subset of a dendroid is called a shore set if there is a sequence of subcontinua disjoint with the given set which converges to the whole continuum. We are dealing with the question when the union of finitely many shore sets is a shore set.
We give a positive answer in the case of planar smooth dendroids and closed disjoint shore sets and we present a simple example of a planar dendroid in which the union of two disjoint closed shore sets is not a shore set. The second result answers a question of A.
Illanes. Finally, we show that the union of a shore point and a closed shore set in a dendroid need not to be a shore set but we prove a positive result in the case of a planar dendroid.