Discrete Localities I

TL;DR

This paper introduces a new theoretical framework called discrete localities, extending the concept of p-local compact groups to provide a broader mathematical structure.

Contribution

It develops the foundational theory of discrete localities, generalizing existing p-local compact groups, and sets the stage for subsequent parts of the series.

Findings

Defines the concept of discrete localities

Establishes basic properties and structures

Lays groundwork for future theoretical developments

Abstract

This is part I of a three-part series of papers, whose aim is to develop a theory of discrete localities. These generalize the p-local compact groups of Broto, Levi, and Oliver.