Definition:Union of Adjacent Open Intervals

Definition
Let $\left({\R, \tau_d}\right)$ be the real number line $\R$ under the usual (Euclidean) topology $\tau_d$.

Let $A$ be the union of the two half-unit open intervals:
 * $A := \left({0 \,.\,.\, \dfrac 1 2}\right) \cup \left({\dfrac 1 2 \,.\,.\, 1}\right)$

Then $\left({A, \tau_d}\right)$ is the union of half-unit open intervals.