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On Carathéodory type multifunctions. (English) Zbl 0851.54020

Summary: Let \(T\), \(X\) and \(Y\) be topological spaces. \({\mathcal P} (Y)\) stands for the family of all nonempty subsets of \(Y\), and \({\mathcal B} (T)\) for the Borel \(\sigma\)-field on \(T\).
In this paper we study multifunctions from \(T \times X\) to \(Y\) which are \({\mathcal B} (T\times X)\)-measurable and semicontinuous in the second variable. We propose a method which allows to obtain some results on such multifunctions from known theorems on semicontinuous multifunctions. As an application of this method, we prove the existence of Carathéodory selectors, some approximation results, and a “sandwich theorem” for multifunctions.

MSC:

54C60 Set-valued maps in general topology
54C65 Selections in general topology
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