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On Borel properties of semi-continuous multifunctions. (English) Zbl 0840.54021
Sufficient conditions for multifunctions to be of lower and of upper Borel class 1 are given. The classes of countably $$R$$-separated and countably $$C$$-separated spaces serve as the range space of multifunctions (they are generalizations of separable metric spaces). Theorem 3 gives sufficient conditions under which the intersection of two upper semi-continuous multifunctions is of upper Borel class 2 (but it is even upper semicontinuous under these conditions). Theorem 4 studies multifunctions with a pointwise dense family of continuous selectors.
##### MSC:
 54C60 Set-valued maps in general topology
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