Spaces allowing Type-2 Complexity Theory revisited

✍ Scribed by Matthias Schröder

• Book ID: 102483069
• Publisher: John Wiley and Sons
• Year: 2004
• Tongue: English
• Weight: 290 KB
• Volume: 50
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200310111

✦ Synopsis

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 onto X. 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)