Computability of semicomputable manifolds in computable topological spaces

2017/01/17 by Iljazović, Zvonko, Sušić, Igor
#FOS: Computer and information sciences #FOS: Mathematics #General Topology (math.GN) #Logic (math.LO) #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.1701.04642

Abstract

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

Related

• Computable structures on topological manifolds
• Strong computable type
• New definitions in the theory of Type 1 computable topological spaces
• Computable Approximations of Semicomputable Graphs
• Computable dyadic subbases and T^ω-representations of compact sets