Computability of 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. 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.
