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A new approach to a hyperspace theory. (English) Zbl 0839.54009

In recent times there has been a spectacular growth in the literature on hyperspaces due to the introduction of several new hypertopologies. Several attempts have been made by Beer and his collaborators as well as by Sonntag and Zalinescu to provide a unified treatment. In this paper the authors use real-valued functions and families of subsets of an arbitrary topological space to give a unified approach to most known hypertopologies. Moreover, this approach yields some new ones, too.

MSC:

54B20 Hyperspaces in general topology
28A10 Real- or complex-valued set functions
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