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Set convergences. An attempt of classification. (English) Zbl 0786.54013

During the last ten years there has been a great interest in hyperspaces – partly due to applications and partly due to interesting new ideas. One of the most prolific researchers in this area is Gerald Beer who has recently written a book on it [Topologies on closed and closed convex sets (Mathematics and its Applications, Vol. 268) Kluwer Acad. Publ. 1993].

The authors of this article have also made valuable contributions to the subject and in this article they explore a new method which allows them not only to derive most of the known hypertopologies but also to define some new ones. In the opinion of the reviewer this article will be of great help not only to the established researchers but also to the newcomers to this field.

MSC:
54B20Hyperspaces (general topology)
54A20Convergence in general topology
54E15Uniform structures and generalizations
54D55Sequential spaces
52A05Convex sets without dimension restrictions (convex geometry)