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Slicings, selections and their applications. (English) Zbl 0780.46008

This important paper contains new techniques for obtaining selection theorems which is based on usage of slicings of a topological space, which is by definition a set-valued mapping of a totally ordered set with closed values. The obtained results are thoroughly contrasted with those of Jayne-Rogers, Ryll-Nardzewski et al.

MSC:

46A55 Convex sets in topological linear spaces; Choquet theory
46B20 Geometry and structure of normed linear spaces
49J27 Existence theories for problems in abstract spaces
49J45 Methods involving semicontinuity and convergence; relaxation
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