Towards a Gleason Cover for Compact Pospaces

TL;DR

This paper introduces a new categorical framework that extends the duality between compact Hausdorff spaces and Gleason spaces to compact pospaces, showing they are quotients of f-spaces.

Contribution

It establishes a new category equivalent to compact pospaces, generalizing existing dualities and linking them to f-spaces.

Findings

Every compact pospace is a quotient of an f-space

New categorical equivalence for compact pospaces

Extension of Gleason space duality

Abstract

We establish a new category equivalent to compact pospaces, and which extend the equivalence between compact Hausdorff spaces and Gleason spaces. As a corollary of this equivalence, we obtain in particular, that every compact pospace is the quotient of an f-space.