Achievement sets and sum ranges with ideal supports
Jacek Marchwicki

TL;DR
This paper introduces and analyzes the concept of ideally supported achievement sets for real series, exploring their complexity, topological properties, and relation to sum ranges, extending classical results like Riemann's theorem.
Contribution
It defines ideal achievement sets, compares them with ideal sum ranges, and completes existing characterizations, providing new generalizations of Riemann's theorem.
Findings
Characterization of ideal achievement sets and their topological properties
Comparison and extension of ideal sum ranges with previous work
Generalization of Riemann's theorem for series with ideal supports
Abstract
We introduce the notion of ideally supported achievement sets for a series of real numbers. We analize their complexity and topological properties. We compare the notion of ideal achievement sets with the notion of ideally supported sum range of real series, considered by Filip\'ow and Szuca. We complete Filip\'ow and Szuca characterization of ideal sum ranges, [R. Filip\'ow, P. Szuca, Rearrangement of conditionally convergent series on a small set, J. Math. Anal. Appl. 362 (2010), no. 1, 64-71.], and we obtain some generalization of Riemann's Theorem.
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.
