Definition:Neighborhood (Topology)/Neighborhood defined as Open
- $N_A$ is a neighborhood of $A$ if and only if $N_A$ is an open set of $T$ which itself contains $A$.
However, this treatment is less common, and considered by many to be old-fashioned.
When the term neighborhood is used on this site, it is assumed to be not necessarily open unless so specified.
The UK English spelling of neighborhood is neighbourhood.