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On closedness assumptions in selection theorems
Repovš, Dušan, 1954- ; Semenov, Pavel Vladimirovič, 1952-
We begin by a short survey of various attempts in selection theory to avoid the closedness assumption for values of multivalued mappings. We collect special cases when Michael's ...▫$G_{\delta}$▫-problem admits an affirmative solution and we prove some unified theorems of such type. We also show that in general this problem has a negative solution. In comparison with a recent result of Filippov, we work directly in the Hilbert cube rather than in the space of all probabilistic measures endowed with different topologies.
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