Germ (mathematics)
In mathematics, the notion of a germ of an object in/on a topological space is an equivalence class of that object and others of the same kind that captures their shared local properties. In particular, the objects in question are mostly functions (or maps) and subsets. In specific implementations of this idea, the functions or subsets in question will have some property, such as being analytic or smooth, but in general this is not needed (the functions in question need not even be continuous); it is however necessary that the space on/in which the object is defined is a topological space, in order that the word local have some sense.
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A-equivalenceAlexander's trickAnalytic continuationBlumenthal's zero–one lawBranched manifoldBrjuno numberCatastrophe theoryCotangent bundleDeformation (mathematics)Differentiable manifoldDirect limitEisenbud–Levine–Khimshiashvili signature formulaExponential sheaf sequenceFunction germGermGerm of a functionGlossary of areas of mathematicsGodement resolutionHaefliger structureHardy fieldIan R. PorteousJ. Arthur Seebach Jr.Jacobian idealJean ÉcalleJet (mathematics)Jet bundleK-equivalenceList of general topology topicsLocal ringLocalization (commutative algebra)Map germMap germsMilnor numberMonodromyMultilinear formNakayama's lemmaNash functionsQuotient ringRegular local ringRinged space
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Germ (mathematics)
In mathematics, the notion of a germ of an object in/on a topological space is an equivalence class of that object and others of the same kind that captures their shared local properties. In particular, the objects in question are mostly functions (or maps) and subsets. In specific implementations of this idea, the functions or subsets in question will have some property, such as being analytic or smooth, but in general this is not needed (the functions in question need not even be continuous); it is however necessary that the space on/in which the object is defined is a topological space, in order that the word local have some sense.
has abstract
In de wiskunde, meer bepaald i ...... gevingen van een gegeven punt.
@nl
In mathematics, the notion of ...... he word local have some sense.
@en
Kiełek funkcji gładkiej w punk ...... pewnym otoczeniu tego punktu.
@pl
La notion de germe en mathémat ...... en théorie des groupes de Lie.
@fr
Росток об'єкта на топологічном ...... их функцій, а лише їх ростків.
@uk
Росток объекта на топологическ ...... а топологическом пространстве.
@ru
数学において、位相空間の中あるいは上の対象の芽(め、が、英: ...... 芽は(局所的に)関数の「心臓 (heart)」であるからだ。
@ja
数学上,一个芽(germ),或称芽胚,是从一个拓扑空间到另一 ...... ation)。黎曼曲面条目中有更多关于那个意义下的芽的细节。
@zh
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first
Evgeniǐ Mikhaǐlovich
@en
id
G/g044390
@en
last
Chirka
@en
title
Germ of smooth functions
@en
Germ
@en
urlname
GermOfSmoothFunctions
@en
wikiPageUsesTemplate
subject
hypernym
comment
In de wiskunde, meer bepaald i ...... gevingen van een gegeven punt.
@nl
In mathematics, the notion of ...... he word local have some sense.
@en
Kiełek funkcji gładkiej w punk ...... pewnym otoczeniu tego punktu.
@pl
La notion de germe en mathémat ...... en théorie des groupes de Lie.
@fr
Росток об'єкта на топологічном ...... их функцій, а лише їх ростків.
@uk
Росток объекта на топологическ ...... а топологическом пространстве.
@ru
数学において、位相空間の中あるいは上の対象の芽(め、が、英: ...... 芽は(局所的に)関数の「心臓 (heart)」であるからだ。
@ja
数学上,一个芽(germ),或称芽胚,是从一个拓扑空间到另一 ...... ation)。黎曼曲面条目中有更多关于那个意义下的芽的细节。
@zh
label
Germ (mathematics)
@en
Germe (mathématiques)
@fr
Germe di funzione
@it
Kiem (wiskunde)
@nl
Kiełek funkcji gładkiej
@pl
Росток (математика)
@ru
Росток (математика)
@uk
芽 (数学)
@ja
芽 (数学)
@zh
싹 (수학)
@ko