Hyperconvexity and endpoints in T₀-quasi-metric spaces

Over the last decades much progress has been made in the investigation of hyperconvexity in metric spaces. Recently Kemajou and others have published an article concerning hyperconvexity in T₀-quasi-metric spaces. In 1964 Isbell introduced and studied the concept of an endpoint of a metric space. The aim of this dissertation is to begin an investigation into hyperconvexity and endpoints of T₀-quasi-metric spaces. It starts off with basic definitions and some well-known properties of quasi-pseudometric spaces. We conclude by commencing an investigation into hyperconvexity and endpoints of T₀-quasi-metric spaces. In this dissertation several results obtained for hyperconvexity and endpoints in metric spaces are generalized to T₀-quasi-metric spaces, and some original results for hyperconvexity and endpoints of T₀-quasi-metric spaces are presented. We also discuss for a partially ordered set the connection between its Dedekind-MacNeille completion and the q-hyperconvex hull of its natural T₀-quasi-metric space.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

2013

Author dc:creator

• Haihambo, Paulus

Advisor dc:contributor.advisor

• Künzi, Hans-Peter A

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/6617

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/6617