Let R be the set of all real numbers and let K={1/n, n is a natural number}. Generate a topology on R by taking as basis all open intervals (a,b) and all sets of the form (a,b)-K (the set of all elements in (a,b) that are not in K). The topology generated is known as the K-topology on R.
K-topology satisfies the Hausdorff axiom. I don't know how to prove it at all. This is my HW. Please help me.