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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.17263 |
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| _version_ | 1866915630959034368 |
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| author | Alroily, Ibtsam A. R. Chaourar, Brahim |
| author_facet | Alroily, Ibtsam A. R. Chaourar, Brahim |
| contents | Let $n$ be a nonnegative integer, and $f(n)$ the number of unlabeled finite topologies on $n$ points. We prove that $f(n+m) \geq f(n) f(m)$ both for the labeled and unlabeled cases. Moreover, we prove a similar inequality for labeled and unlabeled $T_0$ topologies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17263 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A super-multiplicative inequality for the number of finite unlabeled arbitrary and $T_0$ topologies Alroily, Ibtsam A. R. Chaourar, Brahim Combinatorics Primary 05A20, Secondary 05A16, 54B10 Let $n$ be a nonnegative integer, and $f(n)$ the number of unlabeled finite topologies on $n$ points. We prove that $f(n+m) \geq f(n) f(m)$ both for the labeled and unlabeled cases. Moreover, we prove a similar inequality for labeled and unlabeled $T_0$ topologies. |
| title | A super-multiplicative inequality for the number of finite unlabeled arbitrary and $T_0$ topologies |
| topic | Combinatorics Primary 05A20, Secondary 05A16, 54B10 |
| url | https://arxiv.org/abs/2511.17263 |