Homogeneous spaces not separated by arcs
Alexandre Karassev, Vesko Valov

TL;DR
This paper improves previous results by showing that in certain homogeneous metric spaces, regions are not separated by arcs, even under weaker conditions and with only one endpoint of the arc in the interior.
Contribution
The authors extend prior work by weakening the homogeneity condition and considering arcs with only one endpoint in the interior of the region.
Findings
Regions in homogeneous locally compact metric spaces of dimension ≥ 2 are not separated by arcs.
The result holds even when only one arc endpoint is in the interior.
The improvement replaces strong local homogeneity with homogeneity.
Abstract
It was shown by van Mill and Valov that regions in strongly locally homogeneous locally compact metric spaces of dimension are not separated by arcs. We improve this result by replacing strong local homogeneity with homogeneity. Moreover, we prove the result for the case when only one end point of an arc is in the interior of the region.
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 · Advanced Banach Space Theory · Mathematical Dynamics and Fractals
