A Counterexample Regarding C.E. Closed Subsets of [0,1] Under Homeomorphisms
Volker Bosserhoff
TL;DR
This paper presents a specific computably enumerable closed subset of [0,1] that cannot be homeomorphic to any computably compact space, addressing a question in computable topology.
Contribution
It provides the first known counterexample showing that not all c.e. closed subsets of [0,1] are homeomorphic to computably compact spaces.
Findings
Counterexample of a c.e. closed subset not homeomorphic to any computably compact space
Answers an open question by Koh, Melnikov, and Ng
Advances understanding of computable topology and homeomorphism classes
Abstract
We give an example of a computably enumerable closed subset of [0,1] that is not homeomorphic to any computably compact space. This answers a question of Koh, Melnikov and Ng.
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
TopicsComputability, Logic, AI Algorithms · Advanced Topology and Set Theory · Mathematical Dynamics and Fractals