COMPACT MANIFOLDS WITH COMPUTABLE BOUNDARIES
We investigate conditions under which a co-computably enumerable closed set in a computable metric space is computable and prove that in each locally computable computable metric space each co-computably enumerable compact manifold with computable boundary is computable. In fact, we examine the notion of a semi-computable compact set and we prove a more general result: in any computable metric space each semicomputable compact manifold with computable boundary is computable. In particular, each semi-computable compact (boundaryless) manifold is computable.
computable metric space semi-computable compact set computable set co-c.e. set manifold with boundary