1. If $K \subset X$ is compact and $x \in X \setminus K$, then there exist disjoint open sets $U, V \in \tau$ with $x \in U$ and $K \subset V$.
2. If $K_1, K_2 \subset X$ are disjoint compact subsets, then there exist disjoint open sets $U_1, U_2 \in \tau$ with $K_1 \subset U_1$ and $K_2 \subset U_2$.