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Local affine selections of convex multifunctions

Research paper by Szymon Wąsowicz

Indexed on: 08 Nov '16Published on: 08 Nov '16Published in: arXiv - Mathematics - Functional Analysis



Abstract

It is well known that not every convex multifunction admits an affine selection. One could ask whether there exists at least local affine selection. The answer is positive in the finite-dimensional case. The main part of this note consists of two examples of non-existence of local affine selections of convex multifunctions defined on certain infinite-dimensional Banach spaces.