Open Ray is Open in GO-Space

Theorem
Let $\left({S, \preceq, \tau}\right)$ be a generalized ordered space.

Let $p \in S$.

Then:
 * $p^\prec$ and $p^\succ$ are $\tau$-open

where:
 * $p^\prec$ is the strict lower closure of $p$
 * $p^\succ$ is the strict upper closure of $p$.