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Some Results On Quasi-Uniform Spaces, Karen Sylvia Carter

Doctoral Dissertations

"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.

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.

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 …