# Definition:System of Neighborhoods

## Definition

Let $M = \left({A, d}\right)$ be a metric space.

Let $a \in A$.

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

Then $\mathcal N_a$ 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.