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Dictionary:

separate

  (sĕp'ə-rāt') pronunciation

v., -rat·ed, -rat·ing, -rates.

v.tr.
    1. To set or keep apart; disunite.
    2. To space apart; scatter: small farms that were separated one from another by miles of open land.
    3. To sort: separate mail by postal zones.
  1. To differentiate or discriminate between; distinguish: a researcher who separated the various ethnic components of the population sample.
  2. To remove from a mixture or combination; isolate.
  3. To part (a couple), often by decree: She was separated from her husband last year.
  4. To terminate a contractual relationship, as military service, with; discharge.
v.intr.
  1. To come apart.
  2. To withdraw: The state threatened to separate from the Union.
  3. To part company; disperse.
  4. To stop living together as spouses.
  5. To become divided into components or parts: Oil and water tend to separate.
adj. (sĕp'ər-ĭt, sĕp'rĭt)
  1. Set or kept apart; disunited: Libraries often have a separate section for reference books.
    1. Existing as an independent entity.
    2. often Separate Having undergone schism or estrangement from a parent body: Separate churches.
  2. Dissimilar from all others; distinct: “a policeman's way of being separate from you even when he was being nice” (John le Carré).
  3. Not shared; individual: two people who held separate views on the issue.
  4. Archaic. Withdrawn from others; solitary.
n. (sĕp'ər-ĭt, sĕp'rĭt)

A garment, such as a skirt, jacket, or pair of slacks, that may be purchased separately and worn in various combinations with other garments.

[Middle English separaten, from Latin sēparātus, past participle of sēparāre : sē-, apart + parāre, to prepare.]

separately sep'a·rate·ly adv.
separateness sep'a·rate·ness n.

SYNONYMS  separate, divide, part, sever, sunder, divorce. These verbs mean to become or cause to become parted, disconnected, or disunited. Separate applies both to putting apart and to keeping apart: “In the darkness and confusion, the bands of these commanders became separated from each other” (Washington Irving). Divide implies separation by or as if by cutting or splitting into parts or shares; the term often refers to separation into opposing or hostile groups: We divided the orange into segments. “‘A house divided against itself cannot stand.’ I believe this government cannot endure permanently half slave and half free” (Abraham Lincoln). Part refers most often to the separation of closely associated persons or things: “Because … nothing that God or Satan could inflict would have parted us” (Emily Brontë). Sever usually implies abruptness and force: “His head was nearly severed from his body” (H.G. Wells). Sunder stresses violent tearing or wrenching apart: The country was sundered by civil war. Divorce implies complete separation: “a priest and a soldier, two classes of men circumstantially divorced from the kind and homely ties of life” (Robert Louis Stevenson). See also synonyms at distinct.


 
 
Thesaurus: separate

verb

  1. To become or cause to become apart one from another: break, detach, disjoin, disjoint, disunite, divide, divorce, part, split (up). Idioms: part company, set at odds. See assemble/disassemble.
  2. To make a division into parts, sections, or branches: break up, dissever, divide, part, partition, section, segment. See assemble/disassemble, part/whole.
  3. To set apart (one kind or type) from others: sift, sort, winnow. See include/exclude.
  4. To distribute into groups according to kinds: assort, categorize, class, classify, group, pigeonhole, sort (out). See collect/distribute.
  5. To recognize as being different: differentiate, discern, discriminate, distinguish, know, tell. See same/different/compare.
  6. To set apart from a group: close off, cut off, insulate, isolate, seclude, segregate, sequester. See include/exclude.
  7. To terminate a relationship or an association by or as if by leaving one another: break off, break up, part. Informal split (up). Idioms: call it quits, come to a parting of the ways, part company. See assemble/disassemble, continue/stop/pause.
  8. To release from military duty: demobilize, discharge, muster out. See free/unfree, keep/release.

adjective

  1. Being or related to a distinct entity: discrete, individual, particular, single, singular. See include/exclude.
  2. Alone in a given category: lone, one, only, particular, single, singular, sole, solitary, unique. Idioms: first and last, one and only. See include/exclude.
  3. Distinguished from others by nature or qualities: discrete, distinct, several, various. See same/different/compare.

 
Antonyms: separate

adj

Definition: alone, individual
Antonyms: associated, combined, connected, interdependent, joined, mixed, together, united

v

Definition: isolate, segregate
Antonyms: desegregate, join, mix, unite

v

Definition: part company
Antonyms: converge, marry, merge

v

Definition: remove something from group; keep or set apart
Antonyms: bring together, combine, join, mix, unite


 
Word Tutor: separate
pronunciation

IN BRIEF: To keep apart or place apart; to go in different directions; not joined.

pronunciation Ideologies separate us. Dreams and anguish bring us together. — Eugene Ionesco (1912-1994), Romanian-French dramatist.

 
Wikipedia: separated sets

In topology and related branches of mathematics, separated sets are pairs of subsets of a given topological space that are related to each other in a certain way. The notion of when two sets are separated or not is important both to the notion of connected spaces (and their connected components) as well as to the separation axioms for topological spaces.

Separated sets should not be confused with separated spaces (defined below), which are somewhat related but aren't the same thing. And separable spaces are a completely different topological concept.

Definitions

There are various ways in which two subsets of a topological space X can be considered to be separated.

  • A and B are disjoint if their intersection is the empty set. This property has nothing to do with topology as such, but only set theory; we include it here because it is the weakest in the sequence of different notions. For more on disjointness in general, see: disjoint sets.
  • A and B are separated in X if each is disjoint from the other's closure. The closures themselves don't have to be disjoint from each other; for example, the intervals [0,1) and (1,2] are separated in the real line R, even though the point 1 belongs to both of their closures. More generally in any metric space, two open balls Br(x) = {y:d(x,y)<r} and Bs(x) = {y:d(x,y)<s} are separated whenever d(x,y) ≥ r+s. Note that any two separated sets automatically must be disjoint.
  • A and B are separated by neighbourhoods if there are neighbourhoods U of A and V of B such that U and V are disjoint. (Sometimes you will see the requirement that U and V be open neighbourhoods, but this makes no difference in the end.) For the example of A = [0,1) and B = (1,2], you could take U = (-1,1) and V = (1,3). Note that if any two sets are separated by neighbourhoods, then certainly they are separated. If A and B are open and disjoint, then they must be separated by neighbourhoods; just take U := A and V := B. For this reason, separatedness is often used with closed sets (as in the normal separation axiom).
  • A and B are separated by closed neighbourhoods if there are a closed neighbourhood U of A and a closed neighbourhood V of B such that U and V are disjoint. Our examples, [0,1) and (1,2], are not separated by closed neighbourhoods. You could make either U or V closed by including the point 1 in it, but you can't make them both closed while keeping them disjoint. Note that if any two sets are separated by closed neighbourhoods, then certainly they are separated by neighbourhoods.
  • A and B are separated by a function if there exists a continuous function f from the space X to the real line R such that f(A) = {0} and f(B) = {1}. (Sometimes you will see the unit interval [0,1] used in place of R in this definition, but it makes no difference in the end.) In our example, [0,1) and (1,2] are not separated by a function, because there is no way to continuously define f at the point 1. Note that if any two sets are separated by a function, then they are also separated by closed neighbourhoods; the neighbourhoods can be given in terms of the preimage of f as U := f-1[-e,e] and V := f-1[1-e,1+e], as long as e is a positive real number less than 1/2.
  • A and B are precisely separated by a function if there exists a continuous function f from X to R such that f-1(0) = A and f-1(1) = B. (Again, you may also see the unit interval in place of R, and again it makes no difference.) Note that if any two sets are precisely separated by a function, then certainly they are separated by a function. Since {0} and {1} are closed in R, only closed sets are capable of being precisely separated by a function; but just because two sets are closed and separated by a function does not mean that they are automatically precisely separated by a function (even a different function).

Relation to separation axioms and separated spaces

The separation axioms are various conditions that are sometimes imposed upon topological spaces which can be described in terms of the various types of separated sets. As an example, we will define the T2 axiom, which is the condition imposed on separated spaces. Specifically, a topological space is separated if, given any two distinct points x and y, the singleton sets {x} and {y} are separated by neighbourhoods.

Separated spaces are also called Hausdorff spaces or T2 spaces. Further discussion of separated spaces may be found in the article Hausdorff space. General discussion of the various separation axioms is in the article Separation axiom.

Relation to connected spaces

Given a topological space X, it is sometimes useful to consider whether it is possible for a subset A to be separated from its complement. This is certainly true if A is either the empty set or the entire space X, but there may be other possibilities. A topological space X is connected if these are the only two possibilities. Conversely, if a nonempty subset A is separated from its own complement, and if the only subset of A to share this property is the empty set, then A is an open-connected component of X. (In the degenerate case where X is itself the empty set {}, authorities differ on whether {} is connected and whether {} is an open-connected component of itself.)

For more on connected spaces, see Connected space.

Relation to topologically distinguishable points

Given a topological space X, two points x and y are topologically distinguishable if there exists an open set that one point belongs to but the other point does not. If x and y are topologically distinguishable, then the singleton sets {x} and {y} must be disjoint. On the other hand, if the singletons {x} and {y} are separated, then the points x and y must be topologically distinguishable. Thus for singletons, topological distinguishability is a condition in between disjointness and separatedness.

For more about topologically distinguishable points, see Topological distinguishability.


 
Misspellings: separate

Common misspelling(s) of separate

  • seperate

 
Translations: Translations for: Separate

Dansk (Danish)
adj. - adskilt, separat, særlig, enkelt-
v. tr. - adskille, separere, sortere, dele, skille ad
v. intr. - skilles, udskilles, separeres, udtræde
n. - særtryk

Nederlands (Dutch)
(af)scheiden, afzonderen, ontkoppelen, uit elkaar gaan, verschillend, eigen, afzonderlijk, apart, gescheiden

Français (French)
adj. - à part, propre, indépendant, différent, distinct
v. tr. - séparer, diviser, éloigner, dissocier, répartir, trier
v. intr. - se séparer, se détacher, se retirer, se disperser, se diviser
n. - vêtements coordonnés (npl)

Deutsch (German)
v. - (sich) trennen, sich scheiden lassen, spalten, sich abspalten
adj. - verschieden, Sonder..., getrennt, gesondert
n. - Getrennte, (Druckw.) Sonderdruck, Kleid

Ελληνική (Greek)
v. - διαχωρίζω, χωρίζω, ξεχωρίζω
adj. - ξεχωριστός, ξέχωρος, χωριστός, ιδιαίτερος, ανεξάρτητος

Italiano (Italian)
separare, staccare, segregare, separarsi, diverso, separato

Português (Portuguese)
v. - separar
adj. - separado, independente, individual

Русский (Russian)
отдельный, раздельный, сепаратный, особый, отделять, отделяться, различать, разделять, выделять, сортировать, разлучать, расставаться, расходиться, разлагать на части, выделять из раствора, демобилизовывать

Español (Spanish)
adj. - diferente, distinto, separado
v. tr. - separar, disociar, segregar, desenganchar, desacoplar, desconectar, aislar
v. intr. - divorciarse, separarse, desprenderse, despegarse
n. - separata

Svenska (Swedish)
v. - skilja, avskilja, avsöndra, frånskilja, separera, skiljas från varandra, gå skilda vägar
adj. - skild, avskild, enskild, särskild, separat, åtskild

中文(简体) (Chinese (Simplified))
分开的, 单独的, 各别的, 分隔, 使分离, 分割, 使分散, 分开, 分手, 脱离, 分散, 抽印本

中文(繁體) (Chinese (Traditional))
adj. - 分開的, 單獨的, 各別的
v. tr. - 分隔, 使分離, 分割, 使分散
v. intr. - 分開, 分手, 脫離, 分散
n. - 分開, 抽印本

한국어 (Korean)
adj. - 갈라진, 개별적인, 육체를 떠난
v. tr. - 가르다, 별거 시키다, 추출하다
v. intr. - 탈퇴하다, 서로 섞이지 않다, 별거하다
n. - 갈라진 것, 발췌 인쇄, 세퍼릿 (위아래가 따로따로 되어 있는 여성복)

日本語 (Japanese)
v. - 切り離す, 分離する, 分ける, 分離させる, 区切る, 別れる, 別居する
adj. - 分かれた, 離れた, 別々の, 独立した, 個々の

العربيه (Arabic)
‏(فعل) يباعد ما بين, يميز بين, يفصل (صفه) مستقل, منفصل, منعزل‏

עברית (Hebrew)
adj. - ‮נפרד, נבדל, שונה‬
v. tr. - ‮הפריד, הבדיל, חילק, שילח, סילק‬
v. intr. - ‮התפלג, נפרד מ-, פרש‬
n. - ‮תדפיס, פריט מתוך מערכת-ביגוד‬


 
Best of the Web: Separate

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American Sign Language
commtechlab.msu.edu
 
 
 

Did you mean: separate, soil separate (geology), separate, Separates, Separates (1978 Album by 999), Separates [Bonus] (2000 Album by 999)

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Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved.  Read more
Thesaurus. Roget's II: The New Thesaurus, Third Edition by the Editors of the American Heritage® Dictionary Copyright © 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company. All rights reserved.  Read more
Answers Corporation Antonyms. © 1999-2008 by Answers Corporation. All rights reserved.  Read more
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eSpindle provides personalized spelling and vocabulary tutoring online; free trial Read more
Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Separated sets" Read more
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