Mathematics – General Topology
Scientific paper
2009-08-09
J. Math. Anal. Appl. 360:1 (2009), 307-316
Mathematics
General Topology
Scientific paper
10.1016/j.jmaa.2009.06.045
We continue to investigate cases when the Repov\v{s}-Semenov splitting problem for selections has an affirmative solution for continuous set-valued mappings. We consider the situation in infinite-dimensional uniformly convex Banach spaces. We use the notion of Polyak of uniform convexity and modulus of uniform convexity for arbitrary convex sets (not necessary balls). We study general geometric properties of uniformly convex sets. We also obtain an affirmative solution of the splitting problem for selections of certain set-valued mappings with uniformly convex images.
Balashov Maxim V.
Repovš Dušan
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