Scattered $P$-spaces of weight ${\omega }_1$

Abstract

We examine dimensional types of scattered $P$-spaces of weight ${\omega }_1$. Such spaces can be embedded into ${\omega }_2$. There are established similarities between dimensional types of scattered separable metric spaces and dimensional types of $P$-spaces of weight ${\omega }_1$ with Cantor--Bendixson rank less than ${\omega }_1$.