Is R with the cofinite topo1o separable? Prove your answer. Solution Theorem: Let T=(S,?) be a finite complement topology on an infinite set S. Then T is a separable space. Proof: Let S be a set. Then S is countably infinite iff there is a bijection f:S?N, where N is the set of natural numbers. That is, it is an infinite set of the form: {s0,s1,.