Open Interval

Last updated Nov 6, 2022

Let $(T, \leq)$ be a Total Ordering. An Open Interval is $(a,b)$ for $a \leq b \in T$ is the Set $$(a,b) := {x \in T : a < x < b}$$

1. $(a, a) = \emptyset$ for $a \in T$.
2. Sometimes, when referring to an Open Interval, we may include Open Rays and $T$ itself.