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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.
##### MSC:
 54C65 Selections in general topology
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##### References:
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