Point in Topological Space has Neighborhood

Theorem
Let $T = \struct {S, \tau}$ be a topological space.

Let $x \in S$.

Then there exists in $T$ at least one neighborhood of $x$.

That is:
 * $\forall x \in S: \NN_x \ne \O$

where $\NN_x$ is the neighborhood filter of $x$.

Proof
Let $x \in S$.

Then $S$ itself is a neighborhood of $x$.