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arXiv · 2411.17791

Cardinal Sequences of Lindel\"of scattered P-spaces

J. C Martínez·L. Soukup
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Abstract

We continue our investigation of cardinal sequences associated with locally Lindelof, scattered, Hausdorff P-spaces (abbreviated as LLSP spaces). We outline a method for constructing LLSP spaces from cone systems and partial orders with specific properties. Additionally, we establish limitations on the cardinal sequences of LLSP spaces. Finally, we present both a necessary condition and a distinct sufficient condition for a sequence $\langle \kappa_\alpha: \alpha < \omega_2 \rangle$ to be the cardinal sequence of an LLSP space.

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J. C Martínez, L. Soukup. 2024-11-26. Cardinal Sequences of Lindel\"of scattered P-spaces. https://arxiv.org/abs/2411.17791

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