A new approach to $\delta$-rings via Stone duality

TL;DR

This paper introduces Stone $ ext{ extdelta}$-rings, a novel class of $ ext{ extdelta}$-rings, and explores their connections to condensed mathematics and metrizable compact Hausdorff spaces through Stone duality.

Contribution

It defines Stone $ ext{ extdelta}$-rings and establishes their relationship with condensed mathematics, providing new insights into their structure and applications.

Findings

Stone $ ext{ extdelta}$-rings relate to light condensed mathematics

Identifies $ ext{ extdelta}$-rings corresponding to metrizable compact Hausdorff spaces

Establishes duality between $ ext{ extdelta}$-rings and certain topological spaces

Abstract

We define Stone $\delta$-rings as a new class of $\delta$-rings. Via Stone duality, we shows that $\delta$-rings relates light condensed mathematics, which is developed by Clausen-Scholze. Also, we examine some phenomena for this relationship, for example, we observe $\delta$-rings which corresponds to metrizable compact Hausdorff spaces.