Subfitness in distributive (semi)lattices
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910890521001984 |
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| author | Bezhanishvili, Guram Madden, James Moshier, M. Andrew Tressl, Marcus Walters-Wayland, Joanne |
| author_facet | Bezhanishvili, Guram Madden, James Moshier, M. Andrew Tressl, Marcus Walters-Wayland, Joanne |
| contents | We investigate whether the set of subfit elements of a distributive semilattice is an ideal. This question was raised by the second author at the BLAST conference in 2022. We show that in general it has a negative solution, however if the semilattice is a lattice, then the solution is positive. This is somewhat unexpected since, as we show, a semilattice is subfit if and only if so is its distributive lattice envelope. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06071 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subfitness in distributive (semi)lattices Bezhanishvili, Guram Madden, James Moshier, M. Andrew Tressl, Marcus Walters-Wayland, Joanne General Topology 06A12, 06D22, 18F70, 54B35 We investigate whether the set of subfit elements of a distributive semilattice is an ideal. This question was raised by the second author at the BLAST conference in 2022. We show that in general it has a negative solution, however if the semilattice is a lattice, then the solution is positive. This is somewhat unexpected since, as we show, a semilattice is subfit if and only if so is its distributive lattice envelope. |
| title | Subfitness in distributive (semi)lattices |
| topic | General Topology 06A12, 06D22, 18F70, 54B35 |
| url | https://arxiv.org/abs/2404.06071 |