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September 2003 Computable and continuous partial homomorphisms on metric partial algebras
Viggo Stoltenberg-Hansen, John V. Tucker
Bull. Symbolic Logic 9(3): 299-334 (September 2003). DOI: 10.2178/bsl/1058448675

Abstract

We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts are based on numerations and include those of effective metric partial algebras and effective partial homomorphisms. We prove a general equivalence theorem that includes a version of the Pour-El and Richards Theorem, and has other applications. Finally, the Pour-El and Richards axioms for computable sequence structures on Banach spaces are generalised to computable partial sequence structures on metric algebras, and we prove their equivalence with our computability model based on numerations.

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Viggo Stoltenberg-Hansen. John V. Tucker. "Computable and continuous partial homomorphisms on metric partial algebras." Bull. Symbolic Logic 9 (3) 299 - 334, September 2003. https://doi.org/10.2178/bsl/1058448675

Information

Published: September 2003
First available in Project Euclid: 17 July 2003

zbMATH: 1058.03070
MathSciNet: MR2005952
Digital Object Identifier: 10.2178/bsl/1058448675

Rights: Copyright © 2003 Association for Symbolic Logic

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Vol.9 • No. 3 • September 2003
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