Definition:Ray (Order Theory)

Definition
Let $\left({S, \preccurlyeq}\right)$ be a totally ordered set.

Let $\prec$ be the reflexive reduction of $\preccurlyeq$.

Let $a \in S$ be any point in $S$.

Also known as
A ray (either open or closed is also sometimes referred to as a half-line (either open or closed).

The notations:
 * $\left({a \,.\,.\, \to}\right)$ for $a^\succ$
 * $\left({\gets \,.\,.\, a}\right)$ for $a^\prec$
 * $\left[{a \,.\,.\, \to}\right)$ for $a^\succcurlyeq$
 * $\left[{\gets \,.\,.\, a}\right)$ for $a^\preccurlyeq$

can also be used.

Also see

 * Definition:Order Topology: a topology whose sub-basis consists of open rays.