Quasi-uniform type spaces

2019/03/15 by Yaé Ulrich Gaba, Gaba, Yaé Ulrich
Mathematics · #03G25 #06A06 #06F35 #47H05 #47H09 #47H10 #54E35 #54F05 #68Q55 #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN)

paper · pdf · doi:10.48550/arxiv.1903.06582

openalex publication_date 2019/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Künzi'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.

Related

• Topological structure of quasi-partial b-metric-like spaces and some fixed point theorems
• Quasi-metric spaces on which real-valued continuous functions are uniformly continuous
• Partial quasi-metric completeness via Kannan-type fixed points
• Uniform perfectness for quasi-metric spaces
• Fixed point on partial metric type spaces