# Definition:Neighborhood (Neighborhood Space)

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## 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.

## Sources

- 1962: Bert Mendelson:
*Introduction to Topology*... (previous) ... (next): $\S 3.3$: Neighborhoods and Neighborhood Spaces: Definition $3.4$