Closed Ray

Last updated Nov 6, 2022

Let $(T, \leq)$ be a Total Ordering. A Closed Ray is a Set $R \subset T$ of the form $R := {x \in T : x \leq a}$ or $R := {x \in T : x \geq a}$ for some $a \in T$.

1. We denote $[a, \rightarrow) := {x \in T : x \geq a}$ and $(\leftarrow,a] := {x \in T : x \leq a}$.