Banach Spaces as Data Types

We introduce the operators "modified limit" and "accumulation" on a Banach space, and we use this to define what we mean by being internally computable over the space. We prove that any externally computable function from a computable metric space to a computable Banach space is...

Full description

Saved in:
Bibliographic Details
Published inLogical methods in computer science Vol. 7, Issue 2
Main Author Normann, Dag
Format Journal Article
LanguageEnglish
Published Logical Methods in Computer Science e.V 01.01.2011
Subjects
f.1.1, f.4.1, f.3.2
mathematics - logic
Online AccessGet full text
ISSN1860-5974
1860-5974
DOI10.2168/LMCS-7(2:11)2011

Cover

More Information
Summary:We introduce the operators "modified limit" and "accumulation" on a Banach space, and we use this to define what we mean by being internally computable over the space. We prove that any externally computable function from a computable metric space to a computable Banach space is internally computable. We motivate the need for internal concepts of computability by observing that the complexity of the set of finite sets of closed balls with a nonempty intersection is not uniformly hyperarithmetical, and thus that approximating an externally computable function is highly complex.
ISSN:1860-5974
1860-5974
DOI:10.2168/LMCS-7(2:11)2011