Generalization of two theorems of Steinhaus in category bases
Sanjib Basu, Abhit Chandra Pramanik
TL;DR
This paper extends two classical theorems of Steinhaus to the broader context of category bases, revealing new limitations in perfect translation bases where certain Baire sets do not satisfy the extended theorems.
Contribution
It generalizes Steinhaus's theorems to category bases and identifies conditions under which these theorems fail in perfect translation bases.
Findings
Unified two results of Steinhaus in category bases
Extended theorems to broader settings
Identified failure cases in perfect translation bases
Abstract
Here we unify two results of Steinhaus and their corresponding category analogues by extending them in the settings of category bases. We further show that in any perfect translation base, every abundant Baire set contains a full subset for which our second theorem fails.
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 Topology and Set Theory · Computability, Logic, AI Algorithms · Mathematical and Theoretical Analysis