Convergence of sequences of sets. (English) Zbl 0606.54006

Methods of functional analysis in approximation theory, Proc. Int. Conf., Bombay 1985, ISNM 76, 135-155 (1986).
[For the entire collection see Zbl 0592.00021.]
Convergences of sequences of subsets of a metric space X has been variously defined by Hausdorff, Kuratowski, Wijsman, and Mosco. More recently, Brian Fisher [Rostocker Math. Kolloq. 18, 69-78 (1981; Zbl 0479.54025)] has introduced yet another type of sequential convergence of sets (in the context of fixed point theory). According to the authors, ”The aim of this paper is twofold: firstly, we want to put the last kind of convergence in the right place among the other notions indicated above. Secondly, we want to study (F) convergence in some detail.” Actually, most of the article does not pertain to convergence in the sense of Fisher but to the older concepts in the case when X is a normed linear space.
Reviewer: M.Michael


54B20 Hyperspaces in general topology
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)