Computing on the Banach space C[0,1]

Article type: Research Article

Authors: Brown, Tyler A.^{; *}

Affiliations: Division of Health, Mathematics, and Sciences, Columbia College, SC, United States of America. [email protected]

Correspondence: [*] Corresponding author. [email protected].

Abstract: We demonstrate that, within any computable presentation of the Banach space C[0,1], computing 1 is no harder than computing the halting set. Additionally, we prove that the modulus operator |·| is Ø″-computable and use this to show that C[0,1] is Δ30-categorical when we restrict ourselves to the presentations in which at least one homeomorphism of the unit interval onto itself is computable.

Keywords: Banach space, unity, modulus, categoricity

DOI: 10.3233/COM-200306

Journal: Computability, vol. 10, no. 3, pp. 257-270, 2021