A neighborhood of a point is the collection of all the points that are ‘near’ it, with the notion of nearness depending on context.
A neighborhood of a point in a topological space is an open set of the space containing the point.
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/
See also: metric