Abstract
In this chapter (the shortest one in the book) we prove the simplest selection theorem, stated in the title. The proof (see Section 2) remains the proof of Convex-valued theorem, but without any partitions of unity. As in the previous paragraph we begin (see Section 1) by the necessity conditions for solvability of the selection problem for an arbitrary closed-valued mapping. Our proof of Theorem (2.4) follows the original one [257]. The converse theorem (2.1) is a well-known folklore result.
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© 1998 Springer Science+Business Media Dordrecht
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Repovš, D., Semenov, P.V. (1998). Zero-Dimensional Selection Theorem. In: Continuous Selections of Multivalued Mappings. Mathematics and Its Applications, vol 455. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1162-3_3
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DOI: https://doi.org/10.1007/978-94-017-1162-3_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5111-0
Online ISBN: 978-94-017-1162-3
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