Cardinal sequences of Lindelöf scattered P-spaces
Fundamenta Mathematicae
MSC: Primary 54A25; Secondary 54A35, 54D20, 54G10, 54G12, 03E05
DOI: 10.4064/fm240425-22-1
Published online: 18 June 2025
Abstract
We continue our investigation of cardinal sequences associated with locally Lindelöf, scattered, Hausdorff P-spaces (abbreviated as LLSP spaces). We outline a method for constructing LLSP spaces from cone systems 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 $\langle\kappa_{\alpha}:\alpha \lt \omega_2\rangle$ to be the cardinal sequence of an LLSP space.
