open-closed set

См. также в других словарях:

• Closed set — This article is about the complement of an open set. For a set closed under an operation, see closure (mathematics). For other uses, see Closed (disambiguation). In geometry, topology, and related branches of mathematics, a closed set is a set… …   Wikipedia

• closed set — Math. a set that contains all of its accumulation points, as the set of points on and within a circle; a set having an open set as its complement. * * * closed set noun (mathematics) A set in which the result of combining any two members of the… …   Useful english dictionary

• closed set — noun A set whose complement is open. See Also: open set …   Wiktionary

• closed set — Math. a set that contains all of its accumulation points, as the set of points on and within a circle; a set having an open set as its complement. * * * …   Universalium

• open — [ō′pən] adj. [ME < OE, akin to Ger offen < PGmc * upana: for IE base see UP1] 1. a) in a state which permits access, entrance, or exit; not closed, covered, clogged, or shut [open doors] b) closed, but unlocked [the car is open] 2 …   English World dictionary

• closed — S3 [kləuzd US klouzd] adj 1.) not open = ↑shut ≠ ↑open ▪ Make sure all the windows are closed. ▪ She kept her eyes tightly closed. 2.) [not before noun] if a shop, public building etc is closed, it is not open and people cannot enter or use it =… …   Dictionary of contemporary English

• closed — [ klouzd ] adjective ** ▸ 1 covering passage/hole ▸ 2 not doing business ▸ 3 not allowed to everyone ▸ 4 not considering ideas ▸ 5 with fixed number of something ▸ 6 forming complete circle ▸ + PHRASES 1. ) if a door, window, lid, etc. is closed …   Usage of the words and phrases in modern English

• Closed — may refer to: Math Closure (mathematics) Closed manifold Closed orbits Closed set Closed differential form Closed map, a function that is closed. Other Cloister, a closed walkway Closed circuit television Closed, an online community at the social …   Wikipedia

• Open set — Example: The points (x, y) satisfying x2 + y2 = r2 are colored blue. The points (x, y) satisfying x2 + y2 < r2 are colored red. The red points form an open set. The blue points form a closed set. The union of the red and blue points is a… …   Wikipedia

• Open and closed maps — In topology, an open map is a function between two topological spaces which maps open sets to open sets.[1] That is, a function f : X → Y is open if for any open set U in X, the image f(U) is open in Y. Likewise, a closed map is a function… …   Wikipedia

• Closed manifold — See also: Classification of manifolds#Point set In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary. In contexts where no boundary is possible, any compact manifold is a closed manifold.… …   Wikipedia