Continuous approximate roots of polynomial equations via shape theory
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908573039067136 |
|---|---|
| author | Lau, Joshua Marin-Marquez, Vicente |
| author_facet | Lau, Joshua Marin-Marquez, Vicente |
| contents | We study continuous approximate solutions to polynomial equations over the ring $C(X)$ of continuous complex-valued functions over a compact Hausdorff space $X$. We show that when $X$ is one-dimensional, the existence of such approximate solutions is governed by the behaviour of maps from the fundamental pro-group of $X$ into braid groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_01613 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous approximate roots of polynomial equations via shape theory Lau, Joshua Marin-Marquez, Vicente General Topology Logic We study continuous approximate solutions to polynomial equations over the ring $C(X)$ of continuous complex-valued functions over a compact Hausdorff space $X$. We show that when $X$ is one-dimensional, the existence of such approximate solutions is governed by the behaviour of maps from the fundamental pro-group of $X$ into braid groups. |
| title | Continuous approximate roots of polynomial equations via shape theory |
| topic | General Topology Logic |
| url | https://arxiv.org/abs/2510.01613 |