# Definition:Neighborhood (Neighborhood Space)

## Definition

Let $\left({S, \mathcal N}\right)$ be a neighborhood space.

Let $x \in S$.

Let $\mathcal N_x$ satisfy the neighborhood space axioms.

Then each element $N$ of $\mathcal N_x$ is called a neighborhood of $x$.

## Also see

• Results about neighborhoods can be found here.