Application of methods from categorical topolology in orfer to solve problems in the completion theory of quasi-uniform spaces

Models used for the representation of data describe structures on the set of all possible data expressing both qualitative and quantitative information and discribe a notion of continuity for a natural topological structure on the set of data. Continuity with respect to this topology expresses a form of computability. In his paper " Quasi uniformities : reconciling domains with metric spaces" Smyth describes a framework satisfying these demands. He uses quasi-uniform spaces intoduced in the 80's by Fletcher and Lindgren. However there are still some problems. Cartesian closedness is an important property for models used in theoretical informatics and the category of quasi-uniform spaces does not fulfill this property. A second problem is related to the fact that completion theory in the setting of quasi-uniform spaces in not yet settled. We plan to solve both problems by axiomatizing Cauchy filters. This method is inspired by the fact that in the symmetric case by axiomatizing Cauchy filters one ends up with a cartesian closed category, as was shown in our common work together with H.L. Bentley and H. Herrlich. Finally we will develop a completion theory for non-symmetric Cauchy spaces