Combinatorial and model-theoretical principles related to regularity of ultrafilters and compactness of topological spaces. I

TL;DR

This paper explores how infinite matrices influence the compactness of product spaces in topology, linking combinatorial and model-theoretical principles to ultrafilter regularity.

Contribution

It introduces new connections between combinatorial, model-theoretical, and topological principles regarding ultrafilters and compactness.

Findings

Infinite matrices impact ultrafilter regularity.

Compactness of product spaces is affected by these principles.

New theoretical links established between different mathematical areas.

Abstract

We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.