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Spaces allowing Type‐2 Complexity Theory revisited
Author(s) -
Schröder Matthias
Publication year - 2004
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200310111
Subject(s) - mathematics , baire space , class (philosophy) , type (biology) , pure mathematics , topological space , property (philosophy) , computability , type theory , space (punctuation) , representation (politics) , topological tensor product , compact open topology , surjective function , discrete mathematics , algebra over a field , functional analysis , computer science , epistemology , philosophy , artificial intelligence , law , ecology , chemistry , biology , operating system , biochemistry , political science , politics , gene
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)
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