neighborhood

A neighborhood of a point is the collection of all the points that are ‘near’ it, with the notion of nearness depending on context.

Topology

A neighborhood of a point in a topological space is an open set of the space containing the point.

Analysis

An \(\varepsilon\)-neighborhood of a point \(x\) in a metric space is the set of all points of the space whose distance from \(x\) is less than \(\varepsilon\).