Sejam $x, y \in \mathbb{R}$ distintos e $\epsilon = |x - y|$. Considere $A = ]x - \frac{\epsilon}{2}, x + \frac{\epsilon}{2}[$ e $B = ]y - \frac{\epsilon}{2}, y + \frac{\epsilon}{2}[$. Note que $A,B \in \tau_{M}$ $A \cap B = \emptyset$, $x \in A$ e $y \in B$.