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Computable type and computably categorical spaces
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DOI：10.1016/j.jco.2026.102026.png)
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Abstract
En 中文
We examine effective separating sequences on a metric space and, in particular, conditions under which on a metric space every two such sequences are equivalent up to an isometry. Such a metric space is called computably categorical. We prove that an effectively compact metric space (X, d) is computably categorical if the space Iso(X, d) of all isometries of (X, d) has computable type (which in particular holds if Iso(X, d) is a manifold). Using this, we prove that each effectively compact subspace of Euclidean space is computably categorical.
Keywords:
Computable metric space
Effective compactness
Computable type
Computably categorical metric space