# Compact graphings

## TL;DR

This paper introduces a method to transform graphings, which are limit objects of graph sequences, into compact metric spaces with closed edge sets, facilitating analysis of their local and global properties.

## Contribution

It presents a novel procedure for compactifying graphings, enabling better topological and analytical handling of these limit objects.

## Key findings

- Graphings can be embedded into compact metric spaces.
- The edge set becomes closed in the new metric space.
- Nearby points have similar local graph neighborhoods.

## Abstract

Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric space, where the edge set is closed and nearby points have nearby graph neighborhoods.