closed set


closed set
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.

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Universalium. 2010.

Look at other dictionaries:

  • 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

  • Multiplicatively closed set — In abstract algebra, a subset of a ring is said to be multiplicatively closed if it is closed under multiplication (i.e., xy is in the set when x and y are in it) and contains 1 but doesn t contain 0.[1] The condition is especially important in… …   Wikipedia

  • 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

  • closed — /klohzd/, adj. 1. having or forming a boundary or barrier: He was blocked by a closed door. The house had a closed porch. 2. brought to a close; concluded: It was a closed incident with no repercussions. 3. not public; restricted; exclusive: a… …   Universalium

  • 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

  • Closed linear span — In functional analysis, a branch of mathematics, the closed linear span of a set of vectors is the minimal closed set which contains the linear span of that set. Contents 1 Definition 2 Notes 3 A useful lemma …   Wikipedia