Dimensional types and P-spaces

TL;DR

This paper explores the properties of inverse limits of discrete topological spaces, particularly those of height ω₁, and their classification as P-spaces to understand their dimensional types.

Contribution

It introduces a framework for analyzing the dimensional types of inverse limits of discrete spaces of height ω₁ within the class of P-spaces.

Findings

Inverse limits of discrete spaces of height ω₁ are P-spaces.

The study characterizes the dimensional types of these inverse limit spaces.

Provides new insights into the structure of P-spaces derived from inverse systems.

Abstract

We investigate the category of discrete topological spaces, with emphasis on inverse systems of height $\omega_1$. Their inverse limits belong to the class of $P$-spaces, which allows us to explore dimensional types of these spaces.