The notion of a fuzzy metric space due to George and Veeramani has many
advantages in analysis since many notions and results from classical metric space
theory can be extended and generalized to the setting of fuzzy metric spaces, for
instance: the notion of completeness, completion of spaces as well as extension of
maps. The layout of the dissertation is as follows:
Chapter 1 provide the necessary background in the context of metric spaces, while
chapter 2 presents some concepts and results from classical metric spaces in the
setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy
metric spaces, among others we show that: the product of two complete fuzzy metric
spaces is also a complete fuzzy metric space.
Our main contribution is in chapter 4. We introduce the concept of a standard
fuzzy pseudo metric space and present some results on fuzzy metric identification.
Furthermore, we discuss some properties of t-nonexpansive maps. / Mathematical Sciences / M. Sc. (Mathematics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/3224 |
| Date | 12 1900 |
| Creators | Aphane, Maggie |
| Contributors | Moshokoa, Seithuti Philemon |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | 1 online resource (iv, 75 leaves) |
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