Separating covering numbers and separating uniformity numbers of Hausdorff measures need large continuum
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911061819523072 |
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| author | Goto, Tatsuya |
| author_facet | Goto, Tatsuya |
| contents | We show that if $\mathfrak{c} = \aleph_2$ then all covering numbers of Hausdorff measures $\operatorname{cov}(\mathcal{N}^s(\mathbb{R}^d))$ ($0 < s < d, d \in ω$) are equal and all uniformity numbers $\operatorname{non}(\mathcal{N}^s(\mathbb{R}^d))$ ($0 < s < d, d \in ω$) are equal. This is a partial answer to Problem 5.3 and 5.4 of [4]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22592 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Separating covering numbers and separating uniformity numbers of Hausdorff measures need large continuum Goto, Tatsuya Classical Analysis and ODEs Logic 03E17 We show that if $\mathfrak{c} = \aleph_2$ then all covering numbers of Hausdorff measures $\operatorname{cov}(\mathcal{N}^s(\mathbb{R}^d))$ ($0 < s < d, d \in ω$) are equal and all uniformity numbers $\operatorname{non}(\mathcal{N}^s(\mathbb{R}^d))$ ($0 < s < d, d \in ω$) are equal. This is a partial answer to Problem 5.3 and 5.4 of [4]. |
| title | Separating covering numbers and separating uniformity numbers of Hausdorff measures need large continuum |
| topic | Classical Analysis and ODEs Logic 03E17 |
| url | https://arxiv.org/abs/2506.22592 |