 The closed subsets of Z+, equipped with the Appert topology, are the subsets "S" that either contain 1 or for which
As a result, Z+ is a completely normal space (and thus also Hausdorff), for suppose that "A" and "B" are disjoint closed sets.If did not contain 1, then "A" and "B" would also be open and thus completely separated.On the other hand, if "A" contains 1 then "B" is open and formula_5, so that Z+−"B" is an open neighborhood of "A" disjoint from "B".