# Quasi-uniform type spaces

## TL;DR

This paper introduces partial quasi-metric type spaces, extending existing theories of topology, quasi-uniformity, and fixed point theorems to this broader class of spaces.

## Contribution

It generalizes partial quasi-metric and quasi-metric type spaces, extending key theories and fixed point results to this new framework.

## Key findings

- Topological and quasi-uniformity theories extend to partial quasi-metric type spaces.
- Fixed point theorems like Banach, Kannan, Reich, Chatterjea are valid in these spaces.
- Many constructions from K"unzi's theory are successfully generalized.

## Abstract

In this article, we introduce and investigate the concept of partial quasi-metric type space as a generalization of both partial quasi-metric and quasi-metric type spaces. We show that many important constructions studied in K\"unzi's theory of partial quasi-metrics can be successfully extended to these spaces. In particular, we prove that the basic theories of topology and quasi-uniformity are essentially the same for quasi-metric type spaces as for quasi-metric spaces and by extensions, to partial quasi-metric type spaces. We also prove that the Banach, Kannan, Reich and Chatterjea fixed point theorems can be successfully extended to this more general setting.