Can someone say something about my version of "order topology implies Hausdorff"
(WLOG) Let $a <b$, and let $U_1,U_2$ be a neighborhood of $a,b$ respectively. Denote $U_1 = (a - \epsilon, a + \epsilon)$ where $\epsilon = (b - a)/2$. So clearly $U_1 \cap U_2 = \emptyset$.
I am correct right? I just have to one pair of disjoint open sets