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In functional analysis and related areas of mathematics an absorbing set in a vector space is a set which can be "inflated" or "scaled up" to eventually always include any given point of the vector space. Alternative terms are radial or absorbent set. Every neighborhood of the origin in every topological vector space is an absorbing subset.

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rdf:type	Thing
rdfs:label	Absorbierende Menge (de) Absorbing set (en) Ensemble absorbant (fr) 흡수 집합 (ko) 併呑集合 (ja) 吸收集 (zh)
rdfs:comment	In functional analysis and related areas of mathematics an absorbing set in a vector space is a set which can be "inflated" or "scaled up" to eventually always include any given point of the vector space. Alternative terms are radial or absorbent set. Every neighborhood of the origin in every topological vector space is an absorbing subset. (en) Eine absorbierende Menge bezeichnet in der Mathematik eine Teilmenge eines Vektorraumes, die anschaulich so mit Skalaren vergrößert werden kann, dass irgendwann jeder Punkt in ihr enthalten ist und dieser bei weiterer Vergrößerung die Menge auch nicht mehr verlässt. Absorbierende Mengen treten beispielsweise im Kontext von lokalkonvexen Räumen und Minkowski-Funktionalen auf. (de) Une partie d'un espace vectoriel sur un corps valué non discret (par exemple sur R ou C) est dite absorbante lorsque : * Portail des mathématiques (fr) 함수해석학과 수학의 관련 영역에서, 벡터 공간에서 흡수 집합(영어: Absorbing set)은 팽창해서 벡터 공간의 어떤 원소를 포함할 수 있는 집합 S이다. 다른 용어는 또는 흡수성 집합이 있다. (ko) 数学の関数解析学関連分野においてベクトル空間の部分集合が併呑集合（へいどんしゅうごう、英: absorbing set, absorbent set）とは、その部分集合を「膨張」させて空間の任意の点を含むようにできるものを言う。 (ja) 在泛函分析和数学的相关领域中，向量空间中的集合S，如果其可以线性膨胀以包括向量空间中的任意元素，则S被称为吸收集(英語：Absorbing set)。是径向集的特殊情形，有时也被直接称为径向集。 (zh)
rdfs:seeAlso	Topological vector space
dcterms:subject	Functional analysis
Wikipage page ID	1728179 (xsd:integer)
Wikipage revision ID	1120770280 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Barrelled space Bounded set (topological vector space) Unit circle Vector space Complex number Convex set Mathematics Neighbourhood (mathematics) Norm (mathematics) Minkowski functional Locally convex topological vector space Functional analysis Auxiliary normed space Balanced set Banach space Topological vector space Absolute value Absolutely convex set Algebraic interior Field (mathematics) Barrelled set Nonmeager set Graduate Texts in Mathematics Radial set Interval (mathematics) Baire space Functional analysis Metrizable topological vector space Real number Seminorm Set (mathematics) Euclidean topology Symmetric set Unit ball Singleton set Banach disk Semi normed vector space Seminormed space TVS-isomorphism
Link from a Wikipage to an external page	https://archive.org/details/minkowskigeometr0000thom%7Curl-access=registration%7Cseries=Encyclopedia
sameAs	Absorbing set Absorbing set Absorbing set Absorbing set Absorbing set Absorbing set Absorbing set Absorbing set
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