# Definition:Neighborhood (Real Analysis)/Open Subset

## Definition

Let $\alpha \in \R$ be a real number.

Let $N_\alpha$ be a subset of $\R$ which contains (as a subset) an open real set which itself contains (as an element) $\alpha$.

Then $N_\alpha$ is a neighborhood of $\alpha$.

## Linguistic Note

The UK English spelling of neighborhood is neighbourhood.