Some results on quasi-uniform spaces

<p>"An example of a quasi-uniform space which is complete but not strongly complete is constructed. We also give an example to show that a T₁ space does not necessarily have a T₁ strong completion.</p> <p>The definition of Cauchy filter is discussed. An alternate definition, referred to as C-filter, is considered. A construction of a C-completion is given and it is shown that if a quasi-pseudometric is complete, then the corresponding quasi-uniform structure is C-complete.</p> <p>Conjugate quasi-uniform spaces are discussed. A theorem relating a transitive base of a quasi-uniform structure to a transitive base of the conjugate structure is proved. The generation of the fine quasi-uniform structure is discussed.</p> <p>A general method for constructing compatible quasi-uniform structures is obtained. It is shown that the method can be applied to obtain a compatible non-transitive quasi-uniform structure as well as any compatible transitive quasi-uniform structure"--Abstract, page iii.</p>

Name thesis:degree_name

Ph. D. in Mathematics

Grantor

University of Missouri--Rolla

Year dc:date.available

2016

Author dc:creator

• Carter, Karen Sylvia

• Mathematics

Repository record dc:identifier

https://scholarsmine.mst.edu/doctoral_dissertations/191

OAI identifier oai:identifier

oai:scholarsmine.mst.edu:doctoral_dissertations-1193