Title: Computability of semicomputable manifolds in computable topological spaces,
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 $\partial M$ 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.