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arXiv · 2412.20463

Weakly Boolean maximal chains of homeomorphic topologies

Miloš Kurilić·Boriša Kuzeljević
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Abstract

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.

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Miloš Kurilić, Boriša Kuzeljević. 2024-12-29. Weakly Boolean maximal chains of homeomorphic topologies. https://arxiv.org/abs/2412.20463

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