Neighbourhood (mathematics)

For the concept in graph theory, see Neighbourhood (graph theory).

A set in the plane is a neighbourhood of a point if a small disc around is contained in The small disc around is an open set

In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and interior. Intuitively speaking, a neighbourhood of a point is a set of points containing that point where one can move some amount in any direction away from that point without leaving the set.