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In mathematics, an LF-space, also written (LF)-space, is a topological vector space (TVS) X that is a locally convex inductive limit of a countable inductive system of Fréchet spaces. This means that X is a direct limit of a direct system in the category of locally convex topological vector spaces and each is a Fréchet space. The name LF stands for Limit of Fréchet spaces.

Attributes	Values
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rdfs:label	(LF)-Raum (de) LF-space (en) LF空間 (ja)
rdfs:comment	(LF)-Räume sind eine in der Mathematik betrachtete Klasse von Vektorräumen. Abstrahiert man die Konstruktion gewisser Räume aus der Distributionstheorie, so wird man zwanglos auf den Begriff des (LF)-Raums geführt. Dabei handelt es sich um die Vereinigung einer aufsteigenden Folge von Fréchet-Räumen, was man auch als induktiven Limes von Fréchet-Räumen bezeichnet, woher der Name (LF)-Raum rührt. (de) 数学における LF-空間（エルエフくうかん、英: LF-space）は、ベクトル空間の一類で、一口に言えばシュヴァルツ超函数の構成法を抽象化するものである。LF-空間の名は、それがフレシェ空間の増大列の合併（正確には、狭義の可算帰納極限と呼ばれるもの）になっていることに由来する (inductive Limit of F-space)。 (ja) In mathematics, an LF-space, also written (LF)-space, is a topological vector space (TVS) X that is a locally convex inductive limit of a countable inductive system of Fréchet spaces. This means that X is a direct limit of a direct system in the category of locally convex topological vector spaces and each is a Fréchet space. The name LF stands for Limit of Fréchet spaces. (en)
rdfs:seeAlso	Category (mathematics)
dct:subject	Topological vector spaces
Wikipage page ID	2314852 (xsd:integer)
Wikipage revision ID	1101322729 (xsd:integer)
Link from a Wikipage to another Wikipage	Topological embedding Barrelled space Bornological space Topological vector spaces DF-space Initial topology LB-space Mathematics Meager set Nuclear space Fréchet space Locally convex topological vector space Comparison of topologies Functional analysis Topological vector space Distinguished space Hausdorff space Absolutely convex set Alexander Grothendieck F-space Normable Direct limit Directed set Homeomorphism Distribution (mathematics) Final topology Continuous function (topology) Ultrabornological space If and only if Injective function Category (mathematics) Category of topological spaces Locally convex Strong topology LF space Bijective map Algebraic dual space Inductive limit Quasi-barrelled space Quotient map Injective map Bounded map Sequentially continuous Surjective map
sameAs	LF-space LF-space LF-space LF-space LF-space LF-space
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