# Distance Domains: Completeness

## TL;DR

This paper generalizes domain theoretic concepts by replacing transitive relations with non-symmetric distances, extending Smyth completeness and providing multiple characterizations similar to Yoneda completeness.

## Contribution

It introduces a novel framework for domain theory using non-symmetric distances and characterizes Smyth completeness in this new setting.

## Key findings

- Generalization of Smyth completeness with non-symmetric distances
- Multiple characterizations of the extended completeness
- Framework unifies various domain theoretic concepts

## Abstract

We explore extensions of domain theoretic concepts, replacing transitive relations with general non-symmetric distances. These lead to a generalization of Smyth completeness which we characterize in various ways analogous to our previous Yoneda completeness characterizations.