Abstract
The aim of this chapter is to show that the principal properties of values of lower semicontinuous mappings (closedness, convexity,...) are essential in the main selection theorems of §1–§5. In Theorems (6.1), (6.4), (6.5) and (6.10) we follow (with modifications) [258]. Theorem (6.8) is taken from [271] (for another proof see [79]). Example from Theorem (6.7) was constructed in [262]. The remarkable example due to Pixley [331] is the last theorem (6.13) of this chapter and of the Theory.
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© 1998 Springer Science+Business Media Dordrecht
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Repovš, D., Semenov, P.V. (1998). Examples and Counterexamples. In: Continuous Selections of Multivalued Mappings. Mathematics and Its Applications, vol 455. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1162-3_7
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DOI: https://doi.org/10.1007/978-94-017-1162-3_7
Publisher Name: Springer, Dordrecht
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