Scattered $P$-spaces of weight $\omega_1$
Scattered $P$-spaces of weight $\omega_1$
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 $\omega_1$.
\(P\)-space, scattered space, Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces, 54G12, 54F05, 54G10, Scattered spaces, \(P\)-spaces, dimensional type, Mathematics - General Topology
\(P\)-space, scattered space, Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces, 54G12, 54F05, 54G10, Scattered spaces, \(P\)-spaces, dimensional type, Mathematics - General Topology
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