Neighboring mapping points theorem
Metric Geometry
2023-10-04 v5 Algebraic Topology
Combinatorics
Geometric Topology
Abstract
We introduce and study a new family of extensions for the Borsuk-Ulam and topological Radon type theorems. The defining idea for this new family is to replace requirements of the form `a subset that is large in some sense goes to a singleton' with requirements of the milder form `a subset that is large in some sense goes to a subset that is small in some sense'. This approach covers the case of mappings m-sphere to n-space with m<n and extends to wider classes of spaces.
Cite
@article{arxiv.1812.10895,
title = {Neighboring mapping points theorem},
author = {Andrei V. Malyutin and Oleg R. Musin},
journal= {arXiv preprint arXiv:1812.10895},
year = {2023}
}
Comments
21 pages, 5 figures