Some results on quasi-uniform spaces

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