Limit Points in Particular Point Space/Proof 1

Proof
Let $U \in \tau$ be an open set of $T$.

Then by definition of $T$:
 * $p \in U$

That is, $U$ contains (at least) one point of $S$ which is distinct from $x$.

As $U$ is arbitrary, it follows that all open set of $T$ have this property.

The result follows by definition of the limit point of a point.