On quasi-uniform space via strong quasi-uniform covers
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Authors
Ndzinisa, Bonginkhosi Comfort
Issue Date
2024-03
Type
Dissertation
Language
en
Keywords
Quasi-uniform space , Strong quasi-uniform covers , Continuity , Quasi-uniformity , Space , Quasi-uniform structures , Quasi-pseudometric spaces , Completeness , Hausdorff space , Cauchy filter , Transitive , Compact , Natural Sciences (Biotechnological studies) , SDG 4 Quality Education
Alternative Title
Abstract
A quasi-uniformity, unlike a uniformity, is not determined by its quasi-uniform covers.
It is generally known that covering space theory applies to topological spaces that are connected.
In this dissertation, we will define topology induced by strong quasi-uniform cover
which will determine the quasi-uniformity of a quasi-uniform space. And then we will expand
the discussion on strong quasi-uniform covers, detailing how quasi-uniform spaces
via strong quasi-uniform covers give rise to a topological space with some added axioms
which will precisely determine the quasi-uniformity of a given quasi-uniform space.. The
dissertation will further detail on how uniformizable topological spaces are precisely the
completely regular spaces. This erupts from the idea that uniform spaces can be induced
by uniform covers, but in this article, we want to ascertain that the same concept can be
applied with quasi-uniform spaces via strong quasi-uniform covers.