Sur les selecteurs des multifonctions. (On selections of multifunctions). (French) Zbl 0629.54013

The following question appears in specific forms in various fields of mathematics: How “continuous” resp. “measurable” a multifunction F between two sufficiently structured spaces X and Y has to be in order to have a sequence of “continuous” resp. “measurable” selectors \(\{f_ n\}_{n\in {\mathbb{N}}}\) such that \(F(x)=cl\cup^{\infty}_{n=I}f_ n(x)\) for all x in X? The full relevance of this question can be seen in the light of Kuratowski’s “Topology”, of C. Castaing’s 1967 “Thesis” [see also Rev. Franç. Inform. Rech. Opér. 1, 91-126 (1967; Zbl 0153.085)] and of their developments. The reviewed paper gives positive answers to this question for regular topological spaces X and Y while F is either upper semicontinuous and 1-quasi-continuous or it reverses open subsets of Y to Baire subsets of X (Baire measurability). In context, important properties of Baire measurable functions are revealed.
Reviewer: D.Butnariu


54C60 Set-valued maps in general topology
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
54C05 Continuous maps
54C65 Selections in general topology
54C50 Topology of special sets defined by functions


Zbl 0153.085
Full Text: EuDML


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