# Definition:Neighborhood (Neighborhood Space)

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## Definition

Let $\struct {S, \NN}$ be a neighborhood space.

Let $x \in S$.

Let $\NN_x$ satisfy the neighborhood space axioms.

Then each element $N$ of $\NN_x$ is called a **neighborhood** of $x$.

## Also see

- Results about
**neighborhoods**can be found here.

## Sources

- 1975: Bert Mendelson:
*Introduction to Topology*(3rd ed.) ... (previous) ... (next): Chapter $3$: Topological Spaces: $\S 3$: Neighborhoods and Neighborhood Spaces: Definition $3.4$