Covering sponges with tubes
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917096705753088 |
|---|---|
| author | O'Regan, William |
| author_facet | O'Regan, William |
| contents | The aim of this note is to give a short proof of a result of Pyörälä--Shmerkin--Suomala--Wu; the Sierpiński carpet, and generalisations, are tube-null; they can be covered with tubes of arbitrarily small total width. We remark that a more general class of sponge-like sets satisfy this property. For a given $ε> 0$ the proof is able to give an explicit description of the tubes for which the total width is less than $ε.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02374 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Covering sponges with tubes O'Regan, William Classical Analysis and ODEs Dynamical Systems Metric Geometry 05B99, 28A78, 28A80 The aim of this note is to give a short proof of a result of Pyörälä--Shmerkin--Suomala--Wu; the Sierpiński carpet, and generalisations, are tube-null; they can be covered with tubes of arbitrarily small total width. We remark that a more general class of sponge-like sets satisfy this property. For a given $ε> 0$ the proof is able to give an explicit description of the tubes for which the total width is less than $ε.$ |
| title | Covering sponges with tubes |
| topic | Classical Analysis and ODEs Dynamical Systems Metric Geometry 05B99, 28A78, 28A80 |
| url | https://arxiv.org/abs/2501.02374 |