If and only if for all x in X and closed sets C with x not in C, there exists open sets U and V such that x is in U, C is a subset of V and U and V do not intersect
A topological space is simply a set, B, with topology t (see the related link for a definition), and is often denoted as B, t which is similar to how a metric space is often denoted; B, D.
A discrete topology on the integers, Z, is defined by letting every subset of Z be open If that is true then Z is a discrete topological space and it is equipped with a discrete topology. Now is it...