Selections of multifunctions (Q1772990)

The author states the following result: Theorem 4. Let \(F\) be an upper Kuratowski limit of a sequence of the upper Baire continuous compact valued multifunctions \(F_n: X\to Y\), where \(X\) is Baire and \(Y\) is metric compact. Then there are two multifunction \(M_1\), \(M_2\) of \(F\) which are u.s.c. except for a set of first category, \(M_1(x)\subset M_2\subset F(x)\) for any \(x\in X\) and \(M_2= F\) on a residual set. Moreover, \(M_1(M_2)\) can be expressed as upper Kuratowski limit of a sequence of quasi-continuous selections of \(F_n\) (of maximal multifunctions for \(F_n\)). No proof is given.