engleski

Semicomputable manifolds in computable topological spaces

We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable in ambient spaces which are second countable Hausdorff. We prove that a semicomputable compact manifold is computable if its boundary is computable. We also show how this result combined with a certain construction which compactifies a semicomputable set leads to the conclusion that some noncompact semicomputable manifolds in computable metric spaces are computable.

computable metric space ; computable topological space ; semicomputable set ; computable set ; manifold with boundary

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