Neighbourhood (topology)

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 away from that point without leaving the set.

If ${\displaystyle X}$ is a topological space and ${\displaystyle p}$ is a point in ${\displaystyle X}$, a neighbourhood of ${\displaystyle p}$ is a subset ${\displaystyle V}$ of ${\displaystyle X}$ that includes an open set ${\displaystyle U}$ containing ${\displaystyle p}$,

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