Compact spaces with a $\mathbb{P}$-diagonal

TL;DR

This paper proves that any compact Hausdorff space possessing a $ ext{P}$-diagonal property must be metrizable, establishing a significant link between this diagonal condition and metrizability.

Contribution

It demonstrates that the presence of a $ ext{P}$-diagonal in compact Hausdorff spaces guarantees metrizability, a novel result connecting diagonal properties to topological structure.

Findings

Compact Hausdorff spaces with a $ ext{P}$-diagonal are metrizable.

The $ ext{P}$-diagonal condition implies metrizability in this class of spaces.

This result clarifies the relationship between diagonal properties and topological structure.

Abstract

We prove that compact Hausdorff spaces with a $\mathbb{P}$-diagonal are metrizable.