Cardinal functions on continuous images of orderable compacta and applications

TL;DR

This paper investigates the properties of Hausdorff spaces that are continuous images of compact orderable spaces, exploring their structure, embeddings, and applications to Boolean algebras.

Contribution

It provides new structure results and continuum-theoretic embeddings for these spaces, and links their properties to Boolean algebra structures.

Findings

Characterized the relationship between these spaces and compact orderable spaces.

Established continuum-theoretic embedding results.

Connected interval algebras with pseudo-tree algebras.

Abstract

The class of Hausdorff spaces that are continuous images of compact orderable spaces is studied by analyzing the relationship between the elements of this class and compact orderable spaces in a back-and-forth fashion. Structure results for this class are then obtained, as well as continuum-theoretic embedding results. Applications to Boolean algebras are also demonstrated, specifically concerning the relationship between interval algebras and pseudo-tree algebras.