Co-c.e. spheres and cells in computable metric spaces

摘要

We investigate conditions under which a co-computably enumerable set in acomputable metric space is computable. Using higher-dimensional chains andspherical chains we prove that in each computable metric space which is locallycomputable each co-computably enumerable sphere is computable and each co-c.e.cell with co-c.e. boundary sphere is computable.