On the splitting problem for selections

Details On the splitting problem for selections On the splitting problem for selections

2008-07-19

arxiv.org/abs/0807.3104v2

J. Math. Anal. Appl. 355:1 (2009), 277-287.

Mathematics

General Topology

Scientific paper

10.1016/j.jmaa.2009.01.051

We investigate when does the Repov\v{s}-Semenov Splitting problem for selections have an affirmative solution for continuous set-valued mappings in finite-dimensional Banach spaces. We prove that this happens when images of set-valued mappings or even their graphs are P-sets (in the sense of Balashov) or strictly convex sets. We also consider an example which shows that there is no affirmative solution of this problem even in the simplest case in $\R^{3}$. We also obtain affirmative solution of the Approximate splitting problem for Lipschitz continuous selections in the Hilbert space.

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