A lambda-dendroid with two shore points whose union is not a shore set

作者:Pyrih Pavel*; Vejnar Benjamin
来源:Topology and Its Applications, 2012, 159(1): 69-74.
DOI:10.1016/j.topol.2011.07.024

摘要

A subset of a given continuum is called a shore set if there is a sequence of continua in the complement of this set converging to the whole continuum with respect to the Hausdorff metric. A point is called a shore point if the one point set containing this point is a shore set. We present several examples of a lambda-dendroid which contains two disjoint shore continua whose union is not a shore set. This answers a question of Van C. Nall in negative.

  • 出版日期2012-1-1