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Weakly normal topological spaces and upper semicontinuous multifunctions. (Italian. English summary) Zbl 0756.54012

The notion of weakly normal space is introduced. No separation axiom is assumed. A topological space \(X\) is weakly normal if for every pair of disjoint closed sets \(A,B\subset X\) there exist open sets \(U\), \(V\) (containing \(A\) and \(B\) respectively) such that for every closed set \(H\), \(K\), \(H\subset U\) and \(K\subset V\), \(H\cap K=\emptyset\). Weakly normal spaces are investigated in terms of subsets of Cartesian products and upper semicontinuous multifunctions with closed values. A similar characterization is given for normal spaces.
Reviewer: G.Di Maio (Napoli)

MSC:

54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54C60 Set-valued maps in general topology
54C08 Weak and generalized continuity
54B20 Hyperspaces in general topology
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