PRIME

Platonic

Realms

Interactive

Mathematics

Encyclopedia

# 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/

Get the ultimate math study-guide Math & Me: Embracing Success Available in the Math Store

Are you a mathematical artist?

Platonic Realms is preparing an online gallery space to showcase and market the works of painters, sculptors, and other artists working in a tangible medium.

If your work celebrates mathematical themes we want to hear from you!