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 $$\varepsilon$$.