Cardinal Sequences of Lindelöf scattered P-spaces

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 $⟨{\kappa }_{\alpha }:\alpha <{\omega }_2⟩$ to be the cardinal sequence of an LLSP space.