We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
COMPUTABLY ISOMETRIC SPACES.
- Authors
MELNIKOV, ALEXANDER G.
- Abstract
We say that an uncountable metric space is computably categorical if every two computable structures on this space are equivalent up to a computable isometry. We show that Cantor space, the Urysohn space, and every separable Hilbert space are computably categorical, but the space 풞[0, 1] of continuous functions on the unit interval with the supremum metric is not. We also characterize computably categorical subspaces of ℝn. and give a sufficient condition for a space to be computabty categorical. Our interest is motivated by classical and recent results in computable (countable) model theory and computable analysis.
- Subjects
ALGEBRAIC spaces; ALGEBRAIC geometry; ISOMETRIC projection; AXONOMETRIC projection; DESCRIPTIVE geometry
- Publication
Journal of Symbolic Logic, 2013, Vol 78, Issue 4, p1055
- ISSN
0022-4812
- Publication type
Article
- DOI
10.2178/jsl.7804030