Proximal Analysis and Boundaries of Closed Sets in Banach Space. Part II: Applications

Source abstract

This paper is a direct continuation of the article “Proximal analysis and boundaries of closed sets in Banach space, Part I: Theory”, by the same authors. It is devoted to a detailed analysis of applications of the theory presented in the first part and of its limitations. Theorem 2.1 has important consequences for geometry of Banach spaces. We start the presentation with a discussion of density and existence of R -proper points (Definition 1.3) for closed sets in Banach spaces. Our considerations will be based on the “lim inf” inclusions proven in the first part of our paper.