摘要：This article continues the study of computable elementary topology started in [Weihrauch and Grubba 2009]. For computable topological spaces we introduce a number of computable versions of the topological separation axioms T 0, T 1 and T 2. The axioms form an implication chain with many equivalences. By counterexamples we show that most of the remaining implications are proper. In particular, it turns out that computable T 1 is equivalent to computable T 2 and that for spaces without isolated points the hierarchy collapses, that is, the weakest computable T 0 axiom WCT0 is equivalent to the strongest computable T 2 axiom SCT2. The SCT 2-spaces are closed under Cartesian product, this is not true for most of the other classes of spaces. Finally we show that the computable version of a basic axiom for an effective topology in intuitionistic topology is equivalent to SCT2.
关键词：axioms of separation, computable analysis, computable topology
