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    Convexities in t-quasi-metric spaces.

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    Date
    2021
    Author
    Nyirongo, Kennany
    Type
    Thesis
    Language
    en
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    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.
    URI
    http://dspace.unza.zm/handle/123456789/7219
    Publisher
    The University of Zambia
    Subject
    Metric spaces
    Convexities
    Menger convexity
    Description
    Thesis
    Collections
    • Natural Sciences [299]

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