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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2016 | 233 | 2 | 101-141

## Computable structures and operations on the space of continuous functions

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.

101-141

wydano
2016

### Twórcy

• Institute of Natural and Mathematical Sciences, Massey University, Auckland, New Zealand
autor
• Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore