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Generalisations of filters and uniform spaces

The notion of a filter F ∈ 2²x has been extended to that of a : prefilter: ƒ ∈ 1²x, generalised filter ƒ ∈ 2²x x and fuzzy filter ᵩ ∈ 1¹x. A uniformity is a filter with some other conditions and the notion of a uniformity D ∈ 2²xxx has been extended to that of a : fuzzy uniformity d ∈ 1²xxx , generalised uniformity ∈ 1²xxx and super uniformity b ∈ 1¹x. We establish categorical embeddings from the category of uniform spaces into the categories of fuzzy uniform spaces, generalised uniform spaces and super uniform spaces and also categorical embeddings into the category of super uniform spaces from the categories of fuzzy uniform spaces and generalised uniform spaces.

Identiferoai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:rhodes/vital:5409
Date January 1997
CreatorsMuraleetharan, Murugiah
PublisherRhodes University, Faculty of Science, Mathematics
Source SetsSouth African National ETD Portal
LanguageEnglish
Detected LanguageEnglish
TypeThesis, Masters, MSc
Format125 p., pdf
RightsMuraleetharan, Murugiah

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