Abstract
While lower semicontinuity of a mapping with closed convex values is sufficient for the existence of continuous selections, it is, of course, not necessary. For example, one can start by arbitrary continuous singlevalued map f : X→Y and then define F(x) to be a subset of Y such that f (x) ∈ F(x). Then f is a continuous selection for F, but there are no continuity type restrictions for F.
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© 1998 Springer Science+Business Media Dordrecht
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Repovš, D., Semenov, P.V. (1998). Selection Theorems for Non-Lower Semicontinuous Mappings. In: Continuous Selections of Multivalued Mappings. Mathematics and Its Applications, vol 455. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1162-3_11
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DOI: https://doi.org/10.1007/978-94-017-1162-3_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5111-0
Online ISBN: 978-94-017-1162-3
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