A set S is called Hausdorff if for every pair of distinct points x,y in S, there exist open sets Ux containing x and Uy containing y such that the...

A set S is called Hausdorff if for every pair of distinct points x,y in S, there exist open sets Ux containing x and Uy containing y such that the intersection of Ux and Uy is empty.(a) Prove that any set of real numbers is Hausdorff.will leave the best feedback, thanks

Let A ⊂ R, for any a, b ∈ A, we have one real number r ∈ R, such thata < r < b or b < r < awithout loss we can assume a < r < b.Now Let Ua = (−∞, a) ∩ A and Ub =...