Definition:System of Neighborhoods

Definition
Let $M = \struct {A, d}$ be a metric space.

Let $a \in A$.

Let $\NN_a$ be the set of all neighborhoods of $a$ in $M$.

Then $\NN_a$ is the system of neighborhoods of the point $a$.

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