Definition:Union of Adjacent Open Intervals

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

Let $a, b, c \in \R$ where $a < b < c$.

Let $A$ be the union of the two open intervals:
 * $A := \openint a b \cup \openint b c$

Then $\struct {A, \tau_d}$ is the union of adjacent open intervals.