Quasi-uniform type spaces

Yaé Ulrich Gaba

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arXiv · 1903.06582

Quasi-uniform type spaces

Yaé Ulrich Gaba

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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.

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BibTeX RIS

Yaé Ulrich Gaba. 2019-03-15. Quasi-uniform type spaces. https://arxiv.org/abs/1903.06582

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