On Borel properties of semi-continuous multifunctions. (English) Zbl 0840.54021

Spakowski, A.

Acta Univ. Carol., Math. Phys. 35, No. 2, 59-64 (1994).

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.

Reviewer: L’ubica Holá (Bratislava)

MSC:

54C60

Set-valued maps in general topology

Keywords:

countably \(R\)-separated spaces; countably \(C\)-separated spaces