open set

Noun

 * 1)  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.
 * 2)  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.
 * 3)  Most generally, a member of the topology of a given topological space.

Meronyms

 * open ball

Holonyms

 * topology
 * topological space

Related terms

 * closed set

Translations

 * Chinese:
 * Mandarin:
 * Dutch: open verzameling
 * Finnish: avoin joukko
 * French:, ensemble ouvert
 * German: offene Menge
 * Greek: ανοικτό σύνολο
 * Hebrew:
 * Japanese:
 * Macedonian: отворено множество
 * Polish: zbiór otwarty
 * Russian: откры́тое мно́жество
 * Swedish: öppen mängd