Convexities in T0-quasi-metric spaces.
Date
2021
Authors
Nyirongo, Kennany
Journal Title
Journal ISSN
Volume Title
Publisher
The University of Zambia
Abstract
In this thesis, we recall three types of convexities in metric spaces, namely; Menger convexity,
Takahashi convexity andM-convexity. We then generalise these convexities to the framework
of T0-quasi-metric spaces. Since the concept of convexities heavily relies on the concept
of betweenness, a fundamental concept in the study of axiomatic geometry, we begin by
generalising the concept of betweenness to T0-quasi-metric spaces. We show that Takahashi
convexity implies Menger convexity in T0-quasi-metric spaces. Lastly, we generalise the
concept of M-convexity to T0-quasi-metric setting and present some best approximations in
these spaces.
Description
Thesis
Keywords
Metric spaces , Convexities , Menger convexity