Computable structures and operations on the space of continuous functions

• Autorzy: Alexander G. Melnikov , Keng Meng Ng
• Języki publikacji: EN

Abstrakty

EN

We use ideas and machinery of effective algebra to investigate computable structures on the space C[0,1] of continuous functions on the unit interval. We show that (C[0,1],sup) has infinitely many computable structures non-equivalent up to a computable isometry. We also investigate if the usual operations on C[0,1] are necessarily computable in every computable structure on C[0,1]. Among other results, we show that there is a computable structure on C[0,1] which computes + and the scalar multiplication, but does not compute the operation of pointwise multiplication of functions. Another unexpected result is that there exists more than one computable structure making C[0,1] a computable Banach algebra. All our results have implications for the study of the number of computable structures on C[0,1] in various commonly used signatures.

Kategorie tematyczne

• 03F60: Constructive and recursive analysis
• 03C57: Effective and recursion-theoretic model theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 233
• Numer: 2
• Strony: 101-141

Daty

wydano

2016

Twórcy

autor

Alexander G. Melnikov

• Institute of Natural and Mathematical Sciences, Massey University, Auckland, New Zealand

autor

Keng Meng Ng

• Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

Identyfikatory

DOI

10.4064/fm36-12-2015