Theory of representations.

Christoph Kreitz, Klaus Weihrauch.

Theoretical Computer Science 38:35-53, 1985.


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->N} has been developed in a previous paper. By representations from F into 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 T0-space an (up to equivalence) unique admissible representation can be defined which reflects the topological properties correctly.

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Bibtex Entry

@Article{ar:KreitzWeihrauch85a, author = "Christoph Kreitz and Klaus Weihrauch", title = "Theory of representations", journal = "Theoretical Computer Science", volume = 38, year = 1985, pages = "35--53", publisher = ELSEVIER,"Elsevier Science Publishers B.V." }