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 $\omega_1$.