ball

Dictionary: ball¹ (bôl) pronunciation

1. A spherical object or entity: a steel ball.
2. A spherical or almost spherical body: a ball of flame.
Sports.
1. Any of various rounded, movable objects used in various athletic activities and games.
2. Such an object moving, thrown, hit, or kicked in a particular manner: a low ball; a fair ball.
3. A game, especially baseball or basketball, played with such an object.
4. A pitched baseball that does not pass through the strike zone and is not swung at by the batter.
1. A solid spherical or pointed projectile, such as one shot from a cannon.
2. Projectiles of this kind considered as a group.
A rounded part or protuberance, especially of the body: the ball of the foot.
balls Vulgar Slang.
1. The testicles.
2. Courage, especially when reckless.
3. Great presumptuousness.

v., balled, ball·ing, balls.

v.tr.

To form into a ball.
Vulgar Slang. To have sexual intercourse with.

v.intr.

To become formed into a ball.
Vulgar Slang. To have sexual intercourse.

phrasal verb:

ball up

To confuse; bungle.

idiom:

on the ball Informal.

Alert, competent, or efficient: a teacher who is really on the ball.
Relating to qualities, such as competence, skill, or knowledge, that are necessary for success: a manager who has a lot on the ball; a student who has nothing on the ball.

[Middle English bal, probably from Old English *beall.]

ball² (bôl) pronunciation

A formal gathering for social dancing.
Informal. An extremely enjoyable time or experience: We had a ball during our vacation.

[French bal, from Old French, from baller, to dance, from Late Latin ballāre, from Greek ballizein.]

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5min Related Video: ball

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Thesaurus: ball

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noun

dance

Informal

hop

See

work/play

Idioms: ball

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Idioms beginning with ball:
ball and chain
ball of fire
balloon
balloon goes up, the
ballpark figure

See also behind the eight ball; break one's balls; by the balls; carry the ball; crystal ball; drop the ball; eyeball to eyeball; get the ball rolling; have a ball; have one's eye on the ball; have someone by the balls; on the ball; play ball; put in mothballs; snowball's chance in hell; that's how the ball bounces; whole ball of wax.

US Military Dictionary: ball

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n.for small arms ammunition, a solid core bullet for use against targets not requiring armor-piercing or incendiary capability.

See the Introduction, Abbreviations and Pronunciation for further details.

Measures and Units: ball

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oceanography The unit of the Zhubov scale.

Veterinary Dictionary: balling

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The act of administering a bolus or a ball to horses, swine and ruminants for medicinal purposes and to ruminants for identification.

b. gun — a device for administering a bolus to an animal. Consists of a short cylinder sufficiently large to contain the average bolus, a hollow stem containing the rod that connects the handle with the plunger in the cylinder, and the handle. The handle needs to be long enough to position the cylinder in the pharynx before the bolus is discharged by pushing the handle. Sophisticated models have a spring-loaded handle. Suitable for use in horses, cattle, sheep, goats and pigs but a mouth speculum is essential in many uncooperative animals, especially pigs.
b. gun trauma — cellulitis in the pharynx or the cheek opposite the posterior molar teeth caused by too vigorous attempts to push the nozzle of the gun into the pharyngeal orifice.

Word Tutor: ball

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IN BRIEF: A round object that is hit or thrown or kicked in games.

I have learned to hit the ball where it lies. — Unknown from www.zaadz.com.

Tutor's tip: Everyone heard him "bawl" (loud outcry) at the "ball" (formal party with dancing) when his partner stepped on his toe.

Dream Symbol: Ball

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Balls can indicate everything from a game or some other form of relaxation to memories from our childhood. Balls can also have metaphorical connotations, such as being "tossed around," "the ball's in your court," "having a ball" (having a good time) and "having balls" (courage). Any of these may be helpful in determining the meaning of this dream. A deeper, more universal symbolism is that circles and balls represent completeness and wholeness.

Wikipedia: Ball (mathematics)

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A ball is the inside of a sphere

In mathematics, a ball is the inside of a sphere; both concepts apply not only in the three-dimensional space but also for lower and higher dimensions, and for metric spaces in general.

In higher mathematics, a careful distinction is made between the surface of a sphere (referred to as a “sphere”), and the inside of a sphere (referred to as a “ball”). Thus, a sphere in three dimensions is considered to be a two-dimensional spherical surface embedded in three-dimensional Euclidean space, while a ball is a solid figure bounded by a sphere.

1 Balls in general metric spaces
2 Balls in normed vector spaces
3 Topological balls
4 See also
5 References

Balls in general metric spaces

Let (M,d) be a metric space, namely a set M with a metric (distance function) d. The open (metric) ball of radius r > 0 centered at a point p in M, usually denoted by B_r(p) or B(p; r), is defined by

$B_r(p) \triangleq \{ x \in M \mid d(x,p) < r \}.$

The closed (metric) ball, which may be denoted by B_r[p] or B[p; r], is defined by

$B_r[p] \triangleq \{ x \in M \mid d(x,p) \le r \}.$

Note in particular that a ball (open or closed) always includes p itself, since the definition requires r > 0.

The closure of the open ball B_r(p) is usually denoted $\overline{ B_r(p) }$ . While it is always the case that $B_r(p) \subseteq \overline{ B_r(p) }$ and $B_r(p) \subseteq B_r[p]$ , it is not always the case that $\overline{ B_r(p) } = B_r[p]$ . For example, in a metric space $X$ with the discrete metric, one has $\overline{B_1(p)} = \{p\}$ and $B 1 [p] = X$ , for any $p \in X$ .

An (open or closed) unit ball is a ball of radius 1.

A subset of a metric space is bounded if it is contained in some ball. A set is totally bounded if, given any positive radius, it is covered by finitely many balls of that radius.

The open balls of a metric space are a basis for a topological space, whose open sets are all possible unions of open balls. This space is called the topology induced by the metric d.

Balls in normed vector spaces

Any normed vector space V with norm |·| is also a metric space, with the metric d(x, y) = |x − y|. In such spaces, every ball B_r(p) is a copy of the unit ball B₁(0), scaled by r and translated by p.

Euclidean norm

In particular, if V is n-dimensional Euclidean space with the ordinary (Euclidean) metric, every ball is the interior of an hypersphere (a hyperball). That is a bounded interval when n = 1, the interior of a circle (a disk) when n = 2, and the interior of a sphere when n = 3.

P-norm

In Cartesian space $\R^n$ with the p-norm L_p, an open ball is the set

$B(r) = \{ x \in \R^n : \sum_{i=1}^n \left|x_i\right|^p < r^p \}.$

For n=2, in particular, the balls of L₁ (often called the taxicab or Manhattan metric) are squares with the diagonals parallel to the coordinate axes; those of L_∞ (the Chebyshev metric) are squares with the sides parallel to the coordinate axes. For other values of p, the balls are the interiors of Lamé curves (hypoellipses or hyperellipses).

For n = 3, the balls of L₁ are octahedra with axis-aligned body diagonals, those of L_∞ are cubes with axis-aligned edges, and those of L_p with p > 2 are superellipsoids.

General convex norm

More generally, given any centrally symmetric, bounded, open, and convex subset X of Rn, one can define a norm on Rn where the balls are all translated and uniformly scaled copies of X. Note this theorem does not hold if "open" subset is replaced by "closed" subset, because the origin point qualifies but does not define a norm on Rn.

Topological balls

One may talk about balls in any topological space X, not necessarily induced by a metric. An (open or closed) n-dimensional topological ball of X is any subset of X which is homeomorphic to an (open or closed) Euclidean n-ball. Topological n-balls are important in combinatorial topology, as the building blocks of cell complexes.

Any open topological n-ball is homeomorphic to the Cartesian space Rⁿ and to the open unit n-cube $(0,1)^n \subseteq \R^n$ . Any closed topological n-ball is homeomorphic to the closed n-cube [0, 1]ⁿ.

An n-ball is homeomorphic to an m-ball if and only if n = m. The homeomorphisms between an open n-ball B and Rⁿ can be classified in two classes, that can be identified with the two possible topological orientations of B.

A topological n-ball need not be smooth; if it is smooth, it need not be diffeomorphic to a Euclidean n-ball.

References

D. J. Smith and M. K. Vamanamurthy, "How small is a unit ball?", Mathematics Magazine, 62 (1989) 101–107.
"Robin conditions on the Euclidean ball", J. S. Dowker [1]
"Isometries of the space of convex bodies contained in a Euclidean ball", Peter M. Gruber[2]

This section requires expansion.

This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

Donate to Wikimedia

Translations: Ball

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Dansk (Danish)
1.
n. - bold, kugle
v. tr. - forme til kugle
v. intr. - klumpe sammen

idioms:

a ball and chain fodlænke
ball and socket kugleled
ball bearing kugleleje
ball boy bolddreng
ball cock svømmerhane
ball game boldspil
ball girl boldpige
ball lightning kuglelyn
ball printer kuglehovedprinter
ball race kuglering, kugleskål
ball up kludre i, blande sammen
ball valve kugleventil, svømmerventil
be behind the eight ball være i en dårlig position
different ball game en helt anden sag
keep balls in the air holde bolde i luften, have bolde i spil
new ball game en helt anden sag
on the ball kvik, med på den, på bolden
set the ball rolling sætte noget i gang
the ball is in someone's court det er op til nogen, det er nogens udspil
the whole ball of wax hele den forkromede plan

2.
n. - bal

idioms:

have a ball more sig kosteligt, have det sjovt

Nederlands (Dutch)
bal, bol, kogel, pil, worp, pret, balspel, kluwen, prop, vrijen, pret maken, (zich) ballen, (vast) klonteren, samendrommen in de problemen zijn, blut zijn

Français (French)
1.
n. - balle, ballon, bille, boule, (lit, fig) boulet, pelote, peloton, (Culin) boulette, croquette, (Tech) bille de roulement, (Anat) partie antérieure (de la plante du pied), partie charnue (du pouce), globe oculaire, couilles (npl) (vulg), (GB) conneries (npl), courage (npl) (vulg)
v. tr. - mettre en pelote, pelotonner
v. intr. - s'agglomérer

idioms:

ball and chain boulet
ball and socket (joint) à rotule
ball bearing roulement à billes
ball boy ramasseur de balles (tennis)
ball cock robinet à flotteur
ball game jeu de balle/de ballon, (US) match de base-ball
ball girl (Sport) ramasseuse de balles
ball lightning globe de feu, éclair en boule, (fig) (être) débordant d'activité
ball printer imprimante à boules
ball race (Tech) roulement à billes, bille de roulement
ball up semer la pagaille
ball valve valve de ballon
behind the eight ball être un mystère pour, se demander
different ball game (être) une autre paire de manches
keep balls in the air continuer à faire
new ball game (être) une autre paire de manches
on the ball (être) à la hauteur de la situation, ouvrir l'¯il (fam)
set the ball rolling lancer la conversation, débuter quelque chose, démarrer une affaire
the ball is in someone's court (fig) être à qn de jouer, (fig) la balle est dans le camp de qn
the whole ball of wax tout le plan/le projet, toute la chose (etc)

2.
n. - bal, (du) bon temps (arg)

idioms:

have a ball s'amuser comme des fous, se marrer

Deutsch (German)
1.
n. - Kugel, Ball, Knäuel, Bausch
v. - zusammenballen, knüllen

idioms:

ball and chain Hindernis, Klotz am Bein
ball and socket Kugelzapfen
ball bearing Kugellager
ball boy Balljunge
ball cock Schwimmerventil
ball game Ballspiel
ball girl Ballmädchen
ball lightning Kugelblitz
ball printer Balldrucker
ball race Führungsring
ball up vermasseln
ball valve Kugelventil
behind the eight ball unter großem Druck stehen
different ball game eine andere Sache
keep balls in the air etwas in Gang halten
new ball game eine andere Sache
on the ball auf Zack sein
set the ball rolling den Anfang machen
the ball is in someone's court jetzt ist jmd. am Zug
the whole ball of wax der ganze Plan

2.
n. - Ball

idioms:

have a ball sich riesig amüsieren

Ελληνική (Greek)
n. - σφαίρα, μπάλα, τόπι, βλήμα, μπαλιά, μπαλάκι, μπίλια, κουβάρι, χορός, διασκέδαση, ξεφάντωμα, αρχίδι, σαχλαμάρες, κουράγιο
v. - πηδώ (γυναίκα)

idioms:

a ball and chain σιδερένια μπάλα (δεμένη στο πόδι καταδίκου), ασήκωτο βάρος
ball and socket σφαιρική άρθρωση
ball bearing ένσφαιρος τριβέας, ρουλεμάν
ball boy αγόρι που μαζεύει τα μπαλάκια στο τένις
ball cock ρουμπινέτο μπίλιας ή πλωτήρα (φλοτέρ)
ball game παιχνίδι με μπάλα, κατάσταση πραγμάτων
ball girl κορίτσι που μαζεύει τα μπαλάκια του τένις
ball lightning αστραπή σαν πύρινη σφαίρα
ball printer εκτυπωτής με μπαλάκι
ball race δακτύλιος ρουλεμάν
ball up κάνω μαντάρα
ball valve ένσφαιρη βαλβίδα
be behind the eight ball έχω στριμωχτεί, βρίσκομαι σε δύσκολη θέση
different ball game άλλου παπά ευαγγέλιο
have a ball διασκεδάζω φοβερά
keep balls in the air περί πολλά τυρβάζω, διατηρώ τις ισορροπίες
new ball game διαφορετική κατάσταση πραγμάτων
on the ball ξύπνιος, μέσα στα πράγματα
pick up the ball and run αναλαμβάνω πρωτοβουλία
set the ball rolling ξεκινώ μια διαδικασία/συζήτηση
the ball is in someone's court είναι η σειρά του (να κάνει παιχνίδι, να αναλάβει πρωτοβουλία)
the whole ball of wax όλα τα σχετικά

Italiano (Italian)
palla, globo, sfera, pallottola, ballo, lancio, gomitolo, palla di carta straccia

idioms:

a ball and chain palla al piede
a crystal ball sfera di cristallo
ball and socket articolazione sferica
ball bearing cuscinetto a sfere
ball boy raccattapalle
ball cock valvola a galleggiante
ball game gioco di palla
ball girl ragazza raccattapalle
ball lightning fuoco di Sant'Elmo
ball up confondersi
ball valve valvola sferica
be behind the eight ball esitare, essere di fronte ad un enigma
fancydress ball ballo in maschera
have a ball divertirsi da matti
keep balls in the air non concludere nulla
masked ball ballo in maschera
new/different ball game un altro paio di maniche
on the ball in gamba
school ball festa di scuola
set/start the ball rolling mettere in moto
take/pick up the ball and run prendi la palla al balzo
the ball is in someone's court ora sta a...

Português (Portuguese)
n. - bola (f), corpo (m) celeste, jogo (m) de bola, projétil (m) (Mil.), novela (f), fardo (m), baile (m), disparate (m) (fig.)
v. - enovelar, arredondar, aglomerar-se

idioms:

a ball and chain grilhões, impedimento (fig.), esposa (gír.)
a crystal ball bola (f) de cristal
ball and socket articulado (Mec.)
ball bearing rolamento (m) de esferas (Mec.)
ball boy apanhador de bolas em jogos com tênis
ball cock válvula (f) com bóia (Mec.)
ball game partida (f) de beisebol (Esp.)
ball girl apanhadora de bolas em jogos como tênis
ball race partida (f)
ball up confundir
ball valve válvula (f) de esfera (Mec.)
be behind the eight ball estar pela bola sete (coloq.)
fancy dress ball baile (m) à fantasia
have a ball divertir-se muito
keep balls in the air não deixar a peteca cair (coloq.)
masked ball baile (m) de máscaras
new/different ball game experiência ou coisa muito diferente da anterior
on the ball atento, competente
play ball entrar no jogo
school ball baile da escola
set/start the ball rolling dar o pontapé inicial (coloq.)
take/pick up the ball and run pegar a bola e correr
the ball is in someone's court é a vez de outra pessoa agir

Русский (Russian)
шар, шарик, мяч, бал

idioms:

a ball and chain кандалы
a crystal ball хрустальный шар гадалки
ball and socket шарнирное соединение
ball bearing шарикоподшипник
ball boy мальчик подбирающий мячи с теннисной площадки
ball cock поплавковый кран, шаровой кран
ball game игра в мяч, матч
ball girl девочка подбирающая мячи с теннисной площадке
ball lightning шаровая молния
ball race гонка с мячом
ball up заморочить голову, облажаться, завалить
ball valve шаровой клапан
be behind the eight ball находиться в трудном положении
fancy dress ball бал-маскарад
have a ball веселиться до упаду
keep balls in the air одновременно иметь несколько дел
masked ball бал-маскарад
new/different ball game совсем другое дело
on the ball сообразительный, толковый
play ball играть с кем-либо, помогать кому-либо
school ball школьный бал
set/start the ball rolling начать какое-либо дело, заговорить
take/pick up the ball and run пуститься в ход
the ball is in someone's court ты решай

Español (Spanish)
1.
n. - globo, bola, pelota, esfera, bala, balón, ovillo, madeja, bolita de papel
v. tr. - ovillar, apelotonar
v. intr. - ovillarse, apelotonarse, hacerse un ovillo

idioms:

ball and chain una pesada bola de metal ajustada al cuerpo por medio de una cadena, bola de hierro y cadena con que se amarraba a los presidiarios
ball and socket articulación de rótula, articulación universal
ball bearing cojinete de bolas, rodamiento de bolas
ball boy recogepelotas
ball cock llave de bola, grifo de flotador
ball game partido de béisbol, cualquier juego de pelota, situación
ball girl recogepelotas
ball lightning rayo en bola, relámpago en bola
ball printer impresora de bola
ball race anilla de metal de un ruleman donde se colocan los cojinetes
ball up echar a perder, estropear, embrollar
ball valve válvula de flotador
behind the eight ball en posición de desventaja, en dificultades, en una situación problemática
different ball game ahora todo cambia
keep balls in the air tener que ocuparse de varias cosas simultáneamente
new ball game ahora todo cambia
on the ball estar atento, ser espabilado o despierto
set the ball rolling poner las cosas en marcha
the ball is in someone's court ahora le toca jugar a él
the whole ball of wax el total, la totalidad

2.
n. - baile, fiesta social

idioms:

have a ball divertirse, pasarla bien

Svenska (Swedish)
n. - boll, kula, klot, nystan, bal, dans
v. - forma till en boll

中文（简体）(Chinese (Simplified))
1. 球, 人体的球状部位, 球状体, 眼球, 使成球形, 呈球状

idioms:

a ball and chain 锁链, 妻子, 拖累
ball and socket 球窝
ball bearing 滚珠, 滚球轴承, 球轴承
ball boy 球僮
ball cock 浮球阀
ball game 球赛
ball girl 女球僮
ball lightning 球状闪电
ball printer 球式打印机
ball race 球式打印机
ball up 混乱
ball valve 球阀, 弹子阀
be behind the eight ball 受挫, 处于不利地位
different ball game 完全不一样的情况
keep balls in the air 同时进行好几个事情
new ball game 完全是一种新情况
on the ball 机灵, 勤奋, 留心
set the ball rolling 开始活动
the ball is in someone's court 敦促某人作出反应采取行动
the whole ball of wax 所有的东西, 全部情况

2. 舞会, 快乐的时光

idioms:

have a ball 狂欢

中文（繁體）(Chinese (Traditional))
1.
n. - 球, 人體的球狀部位, 球狀體, 眼球
v. tr. - 使成球形
v. intr. - 呈球狀

idioms:

a ball and chain 鎖鏈, 妻子, 拖累
ball and socket 球窩
ball bearing 滾珠, 滾球軸承, 球軸承
ball boy 球僮
ball cock 浮球閥
ball game 球賽
ball girl 女球僮
ball lightning 球狀閃電
ball printer 球式列表機
ball race 球式列表機
ball up 混亂
ball valve 球閥, 彈子閥
be behind the eight ball 受挫, 處於不利地位
different ball game 完全不一樣的情況
keep balls in the air 同時進行好幾個事情
new ball game 完全是一種新情況
on the ball 機靈, 勤奮, 留心
set the ball rolling 開始活動
the ball is in someone's court 敦促某人作出反應採取行動
the whole ball of wax 所有的東西, 全部情況

2.
n. - 舞會, 快樂的時光

idioms:

have a ball 狂歡

한국어 (Korean)
1.
n. - 공, 탄환, 야구
v. tr. - ~을 둥글게 하다
v. intr. - 덩어리가 되다

idioms:

a ball and chain 사슬에 쇠뭉치가 달린 족쇄, 구속, 아내
ball up 뒤범벅을 만들다, 혼란케 하다
be behind the eight ball 위험한 위치에서
keep balls in the air 잘 진행시키다
the ball is in someone's court ~의 책임이다
the whole ball of wax 전체계획[일]

2.
n. - 무도회, 즐거운 한 때

idioms:

have a ball 멋진 시간을 갖다

日本語 (Japanese)
n. - 球, ボール, 球状のもの, 投球, 球技, 弾丸, 舞踏会
v. - 球になる, 球の形にする

idioms:

a ball and chain 束縛するもの
ball and socket 玉継ぎ
ball bearing ボールベアリング
ball boy ボールボーイ
ball cock 浮玉弁
ball game 野球の試合, 球技, 野球, 状況
ball girl ボールガール
ball lightning 球電
ball race レース
ball up 混乱する
ball valve ボール弁
have a ball 楽しく過ごす
new/different ball game 新しい環境
on the ball 油断がない, 能力がある
set/start the ball rolling 始める
take/pick up the ball and run 話を受け継ぐ
the ball is in someone's court 次は～の番だ
wrecking ball 建物解体用の鉄球

العربيه (Arabic)
‏(الاسم) كرة, حفله راقصه (فعل) كور في وضع خاسر‏

עברית (Hebrew)
n. - ‮כדור, כדור משחק, ביצה (אשך)‬
v. tr. - ‮עיגל, כידר‬
v. intr. - ‮התעגל, התכדר‬
n. - ‮נשף ריקודים‬

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Some good "ball" pages on the web:

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mathworld.wolfram.com

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ball	Soccer Ball
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	bb (abbreviation)
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		Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved. Read more
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		Idioms. The American Heritage® Dictionary of Idioms by Christine Ammer. Copyright © 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Company. All rights reserved. Read more
		US Military Dictionary. The Oxford Essential Dictionary of the U.S. Military. Copyright © 2001, 2002 by Oxford University Press, Inc. All rights reserved. Read more
		Measures and Units. A Dictionary of Weights, Measures, and Units. Copyright © Donald Fenna 2002, 2004. All rights reserved. Read more
		Veterinary Dictionary. Saunders Comprehensive Veterinary Dictionary 3rd Edition. Copyright © 2007 by D.C. Blood, V.P. Studdert and C.C. Gay, Elsevier. All rights reserved. Read more
		Word Tutor. Copyright © 2004-present by eSpindle Learning, a 501(c) nonprofit organization. All rights reserved. eSpindle provides personalized spelling and vocabulary tutoring online; free trial. Read more
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ball

Contents

Balls in general metric spaces

Balls in normed vector spaces

Euclidean norm

P-norm

General convex norm

Topological balls

See also

References