Spaces allowing Type‐2 Complexity Theory revisited
Matthias Schröder · Mathematical logic quarterly · 2004
Abstract The basic concept of Type‐2 Theory of Effectivity (TTE) to define computability on topological spaces (X, τ) or limit spaces (X,→) are representations, i. e. surjection functions from the Baire space ontoX. Representations having the topological property of admissibility are known to provide a reasonable computability theory. In this article, we investigate several additional properties of representations which guarantee that such representations induce a reasonable Type‐2 Complexity Theory on the represented spaces. For each of these properties, we give a nice characterization of the class of spaces that are equipped with a representation having the respective property. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)