ETD Collection

Permanent URI for this collectionhttps://wiredspace.wits.ac.za/handle/10539/104


Please note: Digitised content is made available at the best possible quality range, taking into consideration file size and the condition of the original item. These restrictions may sometimes affect the quality of the final published item. For queries regarding content of ETD collection please contact IR specialists by email : IR specialists or Tel : 011 717 4652 / 1954

Follow the link below for important information about Electronic Theses and Dissertations (ETD)

Library Guide about ETD

Browse

Filters

20191

Settings

Author: search.filters.author.Sebogodi, KatlegoSubject: search.filters.subject.Measure theory

Search Results

Now showing 1 - 1 of 1
  • No Thumbnail Available
    Item
    Some topological aspects of modular quasi-metric spaces
    (2019-06) Sebogodi, Katlego
    In this PhD thesis, we present the modular quasi-pseudometric on a nonempty set, a concept that generalises modular pseudometrics to the framework of quasi-metric spaces. We investigate the topological aspects of a set equipped with a modular quasi-pseudometric. It turns out that a set equipped with a modular quasi-pseudometric is a bitopological space in the sense of Kelly. Moreover, we introduce the theory of Isbell-convexity in the setting of modular quasi-pseudometrics which we shall call w-Isbell-convexity. Furthermore, we prove that given a modular set, w-Isbell-convexity is equivalent to Isbellconvexity whenever the modular quasi-pseudometric is continuous from the right on the set of positive numbers. We also study the boundedness of a set endowed with a modular quasi-pseudometric and we shall call it w- boundedness. Consequently, we show that a self w-nonexpansive map in a w-Isbell-convex modular set has a xed point and the set of xed points is w-Isbell-convex whenever the modular quasi-pseudometric is continuous from the right on the set of positive numbers.