On metric spaces with given transfinite asymptotic dimensions
Yan Wu, Jingming Zhu, Taras Radul

TL;DR
This paper constructs metric spaces with specified transfinite asymptotic dimensions, advancing understanding of the structure and properties of such spaces in geometric group theory.
Contribution
It introduces a method to explicitly construct metric spaces with prescribed transfinite asymptotic and complementary-finite asymptotic dimensions.
Findings
Constructed spaces for every countable ordinal with matching dimensions
Demonstrated the existence of spaces with complex transfinite asymptotic structures
Provided new tools for analyzing large-scale geometric properties
Abstract
For every countable ordinal number , we construct a metric space whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both .
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 · Mathematical Dynamics and Fractals · advanced mathematical theories
