
TL;DR
This paper presents an elementary proof demonstrating that every bounded separable metric group can be embedded into a monothetic bounded metric group, highlighting the importance of the boundedness condition.
Contribution
It provides a simplified proof of a known embedding result and emphasizes the necessity of the boundedness assumption.
Findings
Every bounded separable metric group embeds into a monothetic bounded metric group
The boundedness assumption is essential for the embedding result
The proof simplifies understanding of the embedding property in topological groups
Abstract
We provide a very short elementary proof that every bounded separable metric group embeds into a monothetic bounded metric group, in such a way that the result of Morris and Pestov that every separable abelian topological group embeds into a monothetic group is an immediate corollary. We show that the boundedness assumption is essential.
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.
