An approach for a simple, general, and unified theory of effectivity on sets with cardinality not greater than that of the continuum is presented. A standard theory of effectivity on F = {f : N 3 N} has been developed in a previous paper. By representations 6: B--* M this theory is extended to other sets M. Topological and recursion theoretical properties of representations are studied, where the final topology of a representation plays an essential role. It is shown that for any separable T,-space an (up to equivalence) unique admissible representation can be defined which reflects the topological properties correctly.
['Christoph Kreitz', 'Klaus Weihrauch']
Theory of representations