Abstract
There is some inconsistency between statements of the classical selection problems (see Theory) and their solutions. In the category of topological spaces any selection problem is purely a topological question. However, all known solutions of selection problems use a suitable metric structure of the range of the multivalued mapping, i.e. “metric” proofs yield “topological” answers. So, a very natural question arises: Is the (complete) metrizability of the range a necessary condition for existence of a continuous selection?
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© 1998 Springer Science+Business Media Dordrecht
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Repovš, D., Semenov, P.V. (1998). Miscellaneous Results. In: Continuous Selections of Multivalued Mappings. Mathematics and Its Applications, vol 455. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1162-3_13
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DOI: https://doi.org/10.1007/978-94-017-1162-3_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5111-0
Online ISBN: 978-94-017-1162-3
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