article · Logical Methods in Computer Science · 2011

Banach Spaces as Data Types

Cited by 2Open access

Abstract

We introduce the operators "modified limit" and "accumulation" on a Banach space, and we use this to define what we mean by being internally computable over the space. We prove that any externally computable function from a computable metric space to a computable Banach space is internally computable. We motivate the need for internal concepts of computability by observing that the complexity of the set of finite sets of closed balls with a nonempty intersection is not uniformly hyperarithmetical, and thus that approximating an externally computable function is highly complex.

Cite this paper

APA 7

Normann, D. (2011). Banach Spaces as Data Types. Logical Methods in Computer Science, Volume 7, Issue 2. https://doi.org/10.2168/lmcs-7(2:11)2011

MLA 9

Normann, Dag. “Banach Spaces as Data Types.” Logical Methods in Computer Science, vol. Volume 7, Issue 2, 2011, https://doi.org/10.2168/lmcs-7(2:11)2011.

Chicago

Normann, Dag. 2011. “Banach Spaces as Data Types.” Logical Methods in Computer Science Volume 7, Issue 2. https://doi.org/10.2168/lmcs-7(2:11)2011.

Harvard

Normann, D. (2011) ‘Banach Spaces as Data Types’, Logical Methods in Computer Science, Volume 7, Issue 2. Available at: https://doi.org/10.2168/lmcs-7(2:11)2011.

BibTeX

@article{normann2011banach,
  title = {{Banach Spaces as Data Types}},
  author = {Normann, Dag},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 7, Issue 2},
  year = {2011},
  doi = {10.2168/lmcs-7(2:11)2011}
}

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