suspension

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suspension

Fugue No. 4 from J.S. Bach's Well-Tempered Clavier, Book I

1. The act of suspending or the condition of being suspended, especially:
   1. A temporary abrogation or cessation, as of a law or rule.
   2. A temporary debarment, as from school or a privilege, especially as a punishment.
   3. A postponement, as of a judgment, opinion, or decision. See synonyms at pause.
2. Music.
   1. The prolongation of one or more tones of a chord into a following chord to create a temporary dissonance.
   2. The tone so prolonged.
3. A device from which a mechanical part is suspended.
4. The system of springs and other devices that insulates the chassis of a vehicle from shocks transmitted through the wheels.
5. Chemistry. A system in which microscopically visible particles are dispersed throughout a less dense liquid or gas from which they are easily filtered but not easily settled because of system viscocity or molecular interactions.

A mixture in which small solid or liquid particles are suspended in a liquid or gas.

1. Revocation of a bank's charter by a supervisory agency.

2. Bank closing ordered by banking or governmental authorities to control a Run on a bank, or when a bank is declared insolvent.

3. Temporary halt in trading of a security, or trading activity on a stock exchange in advance of a news announcement or to correct an imbalance of buy and sell orders.

4. Debt repayment Moratorium declared by a debtor nation, for example, a temporary halt in interest payments.

noun

1. The condition of being temporarily inactive: abeyance, abeyancy, dormancy, intermission, latency, quiescence. See action/inaction.
2. A cessation of continuity or regularity: break, discontinuance, discontinuation, discontinuity, disruption, interruption, pause. See continue/stop/pause.
3. The act of putting off or the condition of being put off: adjournment, deferment, deferral, delay, postponement, stay¹, waiver. See time.

Definition: delay
Antonyms: completion, continuation, finish, persistence

A mixture of two or more immiscible phases, such as a solid in a liquid or a liquid in a liquid. Suspensions differ from emulsions in that the former usually have to be shaken before each use.

The state in which small particles of an insoluble material are evenly distributed within a fluid such as water or air. Particles may be carried upwards when turbulence outstrips the force of gravity.

In part-writing, a dissonance configuration in which the dissonant or non-harmonic note is tied over from the previous chord (where it occurs in the same part) and resolves by step, usually downwards.

1. temporary cessation, as of pain or a vital process.
2. a supporting from above, as in treatment of spinal disorders.
3. a preparation of a finely divided, undissolved substance dispersed in a liquid vehicle.

• colloid s. — one in which the suspended particles are very small.

In topology, the suspension SX of a topological space X is the quotient space:

Suspension of a circle. The original space is in blue, and the collapsed end points are in green.

of the product of X with the unit interval I = [0, 1]. Intuitively, we make X into a cylinder and collapse both ends to two points. One views X as "suspended" between the end points. One can also view the suspension as two cones on X glued together at their base (or as a quotient of a single cone).

Given a continuous map there is a map defined by Sf([x,t]): = [f(x),t]. This makes S into a functor from the category of topological spaces into itself. In rough terms increases dimension of a space by one: it takes an n-sphere to an (n + 1)-sphere for n ≥ 0.

Note that SX is homeomorphic to the join where S⁰ is a discrete space with two points.

The space SX is sometimes called the unreduced, unbased, or free suspension of X, to distinguish it from the reduced suspension described below.

The suspension can be used to construct a homomorphism of homotopy groups, to which the Freudenthal suspension theorem applies. In homotopy theory, the phenomena which are preserved under suspension, in a suitable sense, make up stable homotopy theory.

Reduced suspension

If X is a pointed space (with basepoint x₀), there is a variation of the suspension which is sometimes more useful. The reduced suspension or based suspension ΣX of X is the quotient space:

.

This is the equivalent to taking SX and collapsing the line (x₀ × I) joining the two ends to a single point. The basepoint of ΣX is the equivalence class of (x₀, 0).

One can show that the reduced suspension of X is homeomorphic to the smash product of X with the unit circle S¹.

For well-behaved spaces, such as CW complexes, the reduced suspension of X is homotopy equivalent to the ordinary suspension.

Σ gives rise to a functor from the category of pointed spaces to itself. An important property of this functor is that it is a left adjoint to the functor Ω taking a (based) space X to its loop space ΩX. In other words,

naturally, where stands for continuous maps which preserve basepoints.

See also

• Cone (topology)
• Join (topology)

References

• Allen Hatcher, Algebraic topology. Cambridge University Presses, Cambridge, 2002. xii+544 pp. ISBN 0-521-79160-X and ISBN 0-521-79540-0
• This article incorporates material from Suspension on PlanetMath, which is licensed under the GFDL.

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

Dansk (Danish)
n. - ophængning, affjedring, standsning, afbrydelse, indstilling, ophævelse, udsættelse, suspension

idioms:

• suspension bridge    hængebro

Nederlands (Dutch)
schorsing, surseance, vering, ophanging

Français (French)
n. - interruption, suspension, (Aut) suspension, (Chim) suspension, (Sport) interruption

idioms:

• suspension bridge    pont suspendu

Deutsch (German)
n. - (zeitweilige) Einstellung, Suspendierung, Suspension, Ausschluß, Aufschub, Aufhängen, Aufhängung, Federung, (mus.) Vorhalt

idioms:

• suspension bridge    Hängebrücke

Ελληνική (Greek)
n. - διαθεσιμότητα, ανάρτηση, κρέμασμα, αναβολή ή αναστολή, εκκρεμότητα, (αθλοπ.) αποβολή (παίκτη), (μηχαν.) ανάρτηση (οχήματος), σύστημα ανάρτησης, (χημ.) αιώρημα

idioms:

• suspension bridge    (αρχιτ.) κρεμαστή γέφυρα

Italiano (Italian)
sospensione

idioms:

• suspension bridge    ponte sospeso

Português (Portuguese)
n. - suspensão (f)

idioms:

• suspension bridge    ponte pênsil

Русский (Russian)
приостановка, приостановление платежей, банкротство, временное прекращение какого-л. жизненного процесса, подвешивание, взвешенное состояние, суспензия, подвеска

idioms:

• suspension bridge    висячий мост

Español (Spanish)
n. - suspensión, aplazo

idioms:

• suspension bridge    puente colgante

Svenska (Swedish)
n. - upphängning, stödjepunkt, suspension, suspendering, avstängning

中文（简体）(Chinese (Simplified))
悬挂, 悬吊, 悬置, 悬浮, 暂停

idioms:

• suspension bridge    吊桥

中文（繁體）(Chinese (Traditional))
n. - 懸掛, 懸吊, 懸置, 懸浮, 暫停

idioms:

• suspension bridge    吊橋

한국어 (Korean)
n. - 매달기, 부유, 미결정

日本語 (Japanese)
n. - 吊るすこと, 懸架装置, 浮遊, 未決, 停職, 停学, 支払い停止

idioms:

• suspension bridge    吊り橋, 吊橋

العربيه (Arabic)
‏(الاسم) حرمان مؤقت من امتياز الخ , ارجاء , تعليق‏

עברית (Hebrew)
n. - ‮תלייה, היות תלוי, עיכוב, דחיית ביצוע, התליה, הפסקה, השעיה, מיתלה, תרחיף, הארכת אקורד כדי שיעמוד בצרימה לאקורד שאחריו‬

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