open set en · NOUN
Meanings
- 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.
- (qualifier: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.
- Most generally, a member of the topology of a given topological space.
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| open sets | Number=Plur | lexicographic |
Deriveds
Holonyms
Meronyms
open ball (in metric spaces)
Relateds
Translations (13)
el ανοικτό σύνολο (the set of all interior points) · ja 開集合 (the set of all interior points) · cmn 開集 /开集 (the set of all interior points) · ru откры́тое мно́жество (the set of all interior points) · sv öppen mängd (the set of all interior points) · fi avoin joukko (the set of all interior points) · de offene Menge (the set of all interior points) · he קבוצה פתוחה (the set of all interior points) · fr ensemble ouvert (the set of all interior points) · fr ouvert (the set of all interior points) · pl zbiór otwarty (the set of all interior points) · nl open verzameling (the set of all interior points) · mk отворено множество (the set of all interior points)