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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 \(\varepsilon\).

Citation Info

  • [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/

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