Definition:Union of Adjacent Open Intervals

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Definition

Let $\left({\R, \tau_d}\right)$ 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:

$A := \left({a \,.\,.\, b}\right) \cup \left({b \,.\,.\, c}\right)$


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


Also see

  • Results about the union of adjacent open intervals can be found here.


Sources