Generalisations of filters and uniform spaces

Muraleetharan, Murugiah (1997) Generalisations of filters and uniform spaces. Masters thesis, Rhodes University.

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Abstract

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.

Item Type:Thesis (Masters)
Uncontrolled Keywords:Prefiter, Generalised filter, Fuzzy filter, Fuzzy uniform space, Uniform space, Embedding functor, Functor isomorphim
Subjects:Q Science > QA Mathematics
Divisions:Faculty > Faculty of Science > Mathematics (Pure & Applied)
Supervisors:Burton, Mike
ID Code:3796
Deposited By: Mrs Carol Perold
Deposited On:24 Oct 2012 08:04
Last Modified:24 Oct 2012 08:04
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