Quasi-uniform type spaces
General Topology
2019-03-18 v1
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.
Cite
@article{arxiv.1903.06582,
title = {Quasi-uniform type spaces},
author = {Yaé Ulrich Gaba},
journal= {arXiv preprint arXiv:1903.06582},
year = {2019}
}