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Quasicontinuous selections for closed-valued multifunctions. (English) Zbl 1005.54020
Let \(X\) be a regular pt-space and \(Y\) a topological one metrizable by a complete metric. If \(F: X \to Y\) is a lower semicontinuous multivalued map with closed values, then \(F\) has a quasicontinuous selection. The notion of a pt-space is introduced in the following way: a topological space is called a pt-space if there is a cover \(\{A_j: j\in J\}\) of \(X\) consisting of pairwise disjoint regularly semiopen sets such that the closure \(\overline {A}_j\) is compact for \(j\in J\). Each Euclidean space \(\mathbb R_n\) is a pt-space.
54C65 Selections in general topology
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