Definition:Neighborhood Filter/Point

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

Let $\NN_x$ be the set of all neighborhoods of $x$ in $T$.

Then $\NN_x$ is the neighborhood filter of $x$ (in $T$).

Also known as
The neighborhood filter of a point can also be referred to as the system of neighborhoods or complete system of neighborhoods at that point.

Also see

 * Neighborhood Filter of Point is Filter