Set-valued mappings

Abstract

Here we deal with some properties of set-valued mappings. These properties will be applied in our further considerations. The notion of a setvalued mapping is a generalization (in a certain sense) of the notion of an ordinary mapping. First, let us recall that a set-valued mapping (or a multi-valued mapping, or a multi-valued function) is a mapping of the type $$F:X \to P(Y)$$ where X and Y are arbitrary sets and the symbol P(Y) denotes the family of all subsets of Y. In other words, for each element x ∈X, we have F (x) ⊆ Y.