"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 proved. The generation of the fine quasi-uniform structure is discussed.
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.
Hicks, Troy L.
Rakestraw, Roy M.
Rigler, A. K.
Stanojevic, Caslav V., 1928-2008
Mathematics and Statistics
Ph. D. in Mathematics
University of Missouri--Rolla
iv, 33 pages
© 1973 Karen Sylvia Carter, All rights reserved.
Dissertation - Open Access
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Carter, Karen Sylvia, "Some results on quasi-uniform spaces" (1973). Doctoral Dissertations. 191.