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Existence of quasicontinuous selections for the space \(2^{\mathbb R}\). (English) Zbl 0863.54014
Let \(X\) be an arbitrary topological space and \(F:X\to \mathbb R\) a continuous multifunction with closed values. Then \(F \) has a quasicontinuous and upper semicontinuous selection such that its discontinuity points form a nowhere dense set. Given an element \((x,y)\) of the graph of \(F\) there is a quasicontinuous and upper semicontinuous selection \(g:X\to \mathbb R\) of \(F\) such that \(g(x)=y\), \(g\) is continuous at \(x\) and its discontinuity points form a nowhere dense set.

MSC:
54C65 Selections in general topology
54C08 Weak and generalized continuity
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