Limits of starshaped sets
This paper discusses relationships among collections of limits of sequences of bounded closed starshaped subsets of a normed linear space E. Three different modes of convergence are considered, one being convergence with respect to the Hausdorff metric. The main results show that the completeness of E, the reflexivity of E, and the finite- dimensionality of E can all be characterized in terms of equality between certain collections of limits of starshaped sets. Also included are necessary and sufficient conditions for the Hausdorff metric limit of a given sequence of sets to be starshaped from a given point.
convergence with respect to the Hausdorff metric
equality between certain collections of limits of starshaped sets
scientific article; zbMATH DE number 3973576
scientific article