Weakly Boolean maximal chains of homeomorphic topologies
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916545350860800 |
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| author | Kurilić, Miloš Kuzeljević, Boriša |
| author_facet | Kurilić, Miloš Kuzeljević, Boriša |
| contents | If $λ<κ$ are infinite cardinals, a linear order $L$ is isomorphic to a maximal chain in $[κ]^{κ|κ}$ (resp. $[κ]^{λ|κ}$; $[κ]^{κ|λ}$) iff $L$ is weakly Boolean, the weight of all initial segments of $L$ is equal to $κ$ (resp. $λ$, $λ^+$) and the weight of all final segments of $L$ is equal to $κ$ (resp. $λ^+$, $λ$). We also provide an application of this result in topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weakly Boolean maximal chains of homeomorphic topologies Kurilić, Miloš Kuzeljević, Boriša Logic 06A06, 06A05, 54A10 If $λ<κ$ are infinite cardinals, a linear order $L$ is isomorphic to a maximal chain in $[κ]^{κ|κ}$ (resp. $[κ]^{λ|κ}$; $[κ]^{κ|λ}$) iff $L$ is weakly Boolean, the weight of all initial segments of $L$ is equal to $κ$ (resp. $λ$, $λ^+$) and the weight of all final segments of $L$ is equal to $κ$ (resp. $λ^+$, $λ$). We also provide an application of this result in topology. |
| title | Weakly Boolean maximal chains of homeomorphic topologies |
| topic | Logic 06A06, 06A05, 54A10 |
| url | https://arxiv.org/abs/2412.20463 |