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Dictionary

Words, grammatical forms and meanings linked to the ontology.

open set en · NOUN

Meanings

  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. (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.
  3. Most generally, a member of the topology of a given topological space.

Forms

SpellingFeaturesLabelsSource
open sets Number=Plur lexicographic

Deriveds

distinguished open set

Holonyms

topology · topological space

Meronyms

open ball (in metric spaces)

Relateds

closed set

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)