# 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 \(\varepsilon\).

- [MLA] “neighborhood.”
*Platonic Realms Interactive Mathematics Encyclopedia.*Platonic Realms, 28 Mar 2013. Web. 28 Mar 2013. <http://platonicrealms.com/> - [APA] neighborhood (28 Mar 2013). Retrieved 28 Mar 2013 from the
*Platonic Realms Interactive Mathematics Encyclopedia:*http://platonicrealms.com/encyclopedia/neighborhood/