Warsaw discs and semicomputability

We examine conditions under which a semicomputable set in a computable metric space is computable. Topology plays an important role in the description of such conditions. Motivated by the known result that a semicomputable cell is computable if its boundary sphere is computable, we investigate semicomputable Warsaw discs and their boundary Warsaw circles. We prove that a semicomputable Warsaw disc is computable if its boundary Warsaw circle is semicomputable.