Enlargements of positive sets
Radu Ioan Bot, Erno Robert Csetnek

TL;DR
This paper explores the concept of enlargements of positive sets in SSD spaces, establishing a framework that links these enlargements to representative functions and extends known results from Banach space theory.
Contribution
It introduces the notion of enlargements for positive sets in SSD spaces, characterizes extremal elements, and connects them to representative functions, extending previous monotone set results.
Findings
Characterization of smallest and largest enlargements in $ ext{E}(A)$
Existence of a bijection between closed enlargements and representative functions
Extension of monotone set results from Banach spaces to SSD spaces
Abstract
In this paper we introduce the notion of enlargement of a positive set in SSD spaces. To a maximally positive set we associate a family of enlargements and characterize the smallest and biggest element in this family with respect to the inclusion relation. We also emphasize the existence of a bijection between the subfamily of closed enlargements of and the family of so-called representative functions of . We show that the extremal elements of the latter family are two functions recently introduced and studied by Stephen Simons. In this way we extend to SSD spaces some former results given for monotone and maximally monotone sets in Banach spaces.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
