Computing on the Banach space C[0,1]
Tyler Brown · Computability · 2021
We demonstrate that, within any computable presentation of the Banach space [Formula: see text], computing [Formula: see text] is no harder than computing the halting set. Additionally, we prove that the modulus operator [Formula: see text] is [Formula: see text]-computable and use this to show that [Formula: see text] is [Formula: see text]-categorical when we restrict ourselves to the presentations in which at least one homeomorphism of the unit interval onto itself is computable.