On fragmentable compact lines
Antonio Avil\'es, Gonzalo Mart\'inez-Cervantes, Grzegorz Plebanek,, Stevo Todorcevic
TL;DR
This paper proves that every fragmentable compact line is also a Radon-Nikodým compact space, establishing a significant connection between these two classes of topological spaces.
Contribution
It demonstrates that fragmentability in compact lines implies Radon-Nikodým compactness, providing a new insight into their structural relationship.
Findings
Fragmentable compact lines are Radon-Nikodým compact spaces.
The result links fragmentability with Radon-Nikodým properties in compact lines.
Establishes a new criterion for Radon-Nikodým compactness in linearly ordered spaces.
Abstract
We prove that if a compact line is fragmentable, then it is a Radon-Nikod\'ym compact space.
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.
Taxonomy
TopicsAdvanced Banach Space Theory · Advanced Topology and Set Theory · Advanced Harmonic Analysis Research