Interior may not equal Exterior of Exterior/Proof 2

Proof
Proof by Counterexample:

Let $\struct {S, \preccurlyeq}$ be a totally ordered set.

Let $T = \struct {S, \tau}$ be the Sorgenfrey line on $\struct {S, \preccurlyeq}$.

Let $A \subseteq S$ denote the subset of $S$ defined as:
 * $A = \openint a {+\infty}$

By Exterior of Exterior in Sorgenfrey Line is not necessarily Interior:
 * $A^{ee} = \hointr a {+\infty}$

while:
 * $A^\circ = \openint a {+\infty}$

The result is apparent.