# open-set

Noun

(*plural* open sets)

- (topology) Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary.
- (topology, analysis, restricted to metric spaces) A set which can be described as an (arbitrary) union of open balls. Equivalently, a set such that for every point in it, there is an open ball centered at that point, such that that open ball is contained by the set.
- (topology) Most generally, a member of the topology of a given topological space.

English Wiktionary. Available under CC-BY-SA license.

Link to this page

Cite this page

**MLA Style**

"open-set." YourDictionary, n.d. Web. 22 May 2018. <http://www.yourdictionary.com/open-set>.

**APA Style**

open-set. (n.d.). Retrieved May 22nd, 2018, from http://www.yourdictionary.com/open-set