Di Bari, Cristina M.; Giovannelli, Nicolò Weakly normal topological spaces and upper semicontinuous multifunctions. (Italian. English summary) Zbl 0756.54012 Atti Semin. Mat. Fis. Univ. Modena 39, No. 1, 1-9 (1991). 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) Cited in 1 Document 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 Keywords:weakly normal space; upper semicontinuous multifunctions PDFBibTeX XMLCite \textit{C. M. Di Bari} and \textit{N. Giovannelli}, Atti Semin. Mat. Fis. Univ. Modena 39, No. 1, 1--9 (1991; Zbl 0756.54012)