A convex-valued selection theorem with a non-separable Banach space

Advances in Nonlinear Analysis

article

Pascal Gourdel¹  Nadia Mâagli¹ 

[1] Paris School of Economics, Université Paris 1 Panthéon–Sorbonne, Centre d’Economie de la Sorbonne–CNRS, 106-112 Boulevard de l’Hôpital

关键词: Barycentric coordinates;    continuous selections;    lower semicontinuous correspondence;    closed-valued correspondence;    finite-dimensional convex values;    separable Banach spaces;   

DOI  :  10.1515/anona-2016-0053

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

In the spirit of Michael’s selection theorem [6, Theorem 3.1”’], we consider a nonempty convex-valued lower semicontinuous correspondence φ:X→2Y{\varphi:X\to 2^{Y}}. We prove that if φ has either closed or finite-dimensional images, then there admits a continuous single-valued selection, where X is a metric space and Y is a Banach space. We provide a geometric and constructive proof of our main result based on the concept of peeling introduced in this paper.

【 授权许可】

CC BY