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In mathematics, particularly in functional analysis, a bornological space is a type of space which, in some sense, possesses the minimum amount of structure needed to address questions of boundedness of sets and linear maps, in the same way that a topological space possesses the minimum amount of structure needed to address questions of continuity. Bornological spaces are distinguished by the property that a linear map from a bornological space into any locally convex spaces is continuous if and only if it is a bounded linear operator.

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rdf:type	yago:WikicatTopologicalVectorSpaces yago:Abstraction100002137 yago:Attribute100024264 yago:Possession100032613 yago:Property113244109 yago:Relation100031921 yago:Space100028651 yago:WikicatPropertiesOfTopologicalSpaces
rdfs:label	Bornologischer Raum (de) Bornological space (en) 有界型空間 (ja) 유계형 집합 (ko)
rdfs:comment	Bornologische Räume sind in dem mathematischen Teilgebiet Funktionalanalysis spezielle lokalkonvexe Räume, für deren lineare Operatoren die aus der Theorie der normierten Räume bekannte Äquivalenz von Stetigkeit und Beschränktheit gilt. Diese Räume lassen sich durch ihre Nullumgebungsbasen charakterisieren und haben weitere Eigenschaften mit normierten Räumen gemeinsam. (de) 수학에서 유계형 집합(有界型集合, 영어: bornological set)은 유계 부분 집합들의 집합족이 명시된 집합이다. (ko) 数学、特に函数解析学における有界型空間（ゆうかいけいくうかん、ゆうかいがたくうかん界相空間（かいそうくうかん、英: bornological space; ボルノロジー空間）は、集合や函数の有界性の問題をある意味で考えるのに最低限必要な構造というものを抽出した空間のクラスである（これは位相空間が連続性の問題を考えるのに最低限必要な構造を抽出したものであったことと同様の考え方である）。界相空間を初めて考えたのはマッキーで、命名はブルバキによる（フランス語で有界を意味する borné (と位相 topology) に由来）。 (ja) In mathematics, particularly in functional analysis, a bornological space is a type of space which, in some sense, possesses the minimum amount of structure needed to address questions of boundedness of sets and linear maps, in the same way that a topological space possesses the minimum amount of structure needed to address questions of continuity. Bornological spaces are distinguished by the property that a linear map from a bornological space into any locally convex spaces is continuous if and only if it is a bounded linear operator. (en)
name	Theorem (en) Mackey-Ulam theorem (en)
dcterms:subject	Topological vector spaces
Wikipage page ID	1804457 (xsd:integer)
Wikipage revision ID	1124682504 (xsd:integer)
Link from a Wikipage to another Wikipage	Quasi-complete Montel space Valued field Barrelled space Bounded set (topological vector space) Topological vector spaces LB-space Complete topological vector space Continuous dual Continuous linear operator Convex set Mathematics Separable space Fréchet space George Mackey Bounded set Minkowski functional Convex hull Locally convex space Locally convex topological vector space Functional analysis Mackey space Mackey topology Balanced hull Balanced set Banach space Topological vector space Topologies on spaces of linear maps Distinguished space Hausdorff space Absolutely convex set American Mathematical Society F-space Field (mathematics) Nicolas Bourbaki Normed space Absorbing set LF-space Bornivorous set Ultrabornological space Infrabarreled space Metrizable topological vector space Neighborhood basis Reflexive space Seminorm Sequential space Locally convex Topological space Strong dual space Bornivorous Quasi-barrelled Continuous map (topology) Banach disk Bounded linear operator Seminormed space Ulam measure
sameAs	Bornological space Bornological space Bornological space Bornological space Bornological space Bornological space Bornological space
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