In mathematics, particularly in functional analysis, a bornological space is a type of space which, in some sense, possesses the minimum amount of structure...
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Bounded operator (section Bornological spaces)
normed space). Bornological spaces are exactly those locally convex spaces for which every bounded linear operator into another locally convex space is necessarily...
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Local boundedness (section Topological vector spaces)
bounded. Bornological space – Space where bounded operators are continuous Bounded operator – Linear transformation between topological vector spaces Bounded...
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quasi-ultrabarrelled space, and a bornological space but there exist bornological spaces that are not ultrabornological. Every ultrabornological space X {\displaystyle...
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Bornology (redirect from Bornological set)
of the key motivations behind bornologies and bornological analysis is the fact that bornological spaces provide a convenient setting for homological algebra...
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a Fréchet space. The strong dual of a reflexive Fréchet space is a bornological space and a Ptak space. Every Fréchet space is a Ptak space. The strong...
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Barrelled space Bornological space Bourbaki–Alaoglu theorem Dual pair F-space Fréchet space Krein–Milman theorem Locally convex topological vector space Mackey...
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normed space) is bounded if and only if it is continuous. The same is true of a linear map from a bornological space into a locally convex space. Guaranteeing...
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Bornological space – Space where bounded operators are continuous Bounded linear operator – Linear transformation between topological vector spacesPages...
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locally convex space, then the strong dual of X {\displaystyle X} is a bornological space if and only if it is an infrabarreled space, if and only if...
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0<p<1.} Barrelled spaces: locally convex spaces where the Banach–Steinhaus theorem holds. Bornological space: a locally convex space where the continuous...
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quasibarrelled DF-space that is not bornological. There exists a quasibarrelled space that is not a σ-barrelled space. Barrelled space – Type of topological...
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Distribution (mathematics) (redirect from Distribution space)
reflexive nuclear Montel bornological barrelled Mackey space; the same is true of its strong dual space (that is, the space of all distributions with...
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particular, the strong dual of a bornological space is complete. However, it need not be bornological. Every quasi-complete DF-space is complete. Let ω {\displaystyle...
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convex space is continuous. The space ( X , τ lc ) {\displaystyle \left(X,\tau _{\operatorname {lc} }\right)} is a bornological space. Every normed space is...
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Montel spaces having closed vector subspaces that are not Montel spaces. Barrelled space – Type of topological vector space Bornological space – Space where...
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{\displaystyle 0_{R}} such that w A ⊆ B . {\displaystyle wA\subseteq B.} Bornological space – Space where bounded operators are continuous Bornivorous set – A set...
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each of these three spaces, are complete nuclear Montel bornological spaces, which implies that all six of these locally convex spaces are also paracompact...
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variable Publisher: R. E. Krieger Pub. Co (1977) ISBN 0-88275-531-5 Bornological space "George Mackey - The Mathematics Genealogy Project". www.mathgenealogy...
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DF-space is a Fréchet space. The strong dual of a reflexive Fréchet space is a bornological space. The strong bidual (that is, the strong dual space of...
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families are independence systems, greedoids, antimatroids, and bornological spaces. Algebra of sets – Identities and relationships involving sets Class...
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spaces that are Mackey spaces include: All barrelled spaces and more generally all infrabarreled spaces Hence in particular all bornological spaces and...
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spaces. The category of Fréchet spaces. The category of (Hausdorff) bornological spaces. These will give you an idea of what to think of; for more examples...
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Bornological space – Space where bounded operators are continuous Injective tensor product Locally convex topological vector space – A vector space with...
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bornological space. All normed spaces and semi-reflexive spaces are distinguished spaces. LF spaces are distinguished spaces. The strong dual space X...
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Polar topology (category Topology of function spaces)
X . {\displaystyle X.} If X {\displaystyle X} is a bornological space (e.g. metrizable or LF-space) then X b ( X ′ , X ) ′ {\displaystyle X'_{b(X',X)}}...
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Bornivorous set (category Topological vector spaces)
the definitions of many classes of topological vector spaces, particularly bornological spaces. If X {\displaystyle X} is a TVS then a subset S {\displaystyle...
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convex spaces (such as Fréchet spaces) is necessarily complete. In particular, every LF-space is complete. Every LF-space is barrelled and bornological, which...
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linear operator between Banach spaces for which the image of the unit ball is bounded. bornological A bornological space. Birkhoff orthogonality Two vectors...
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Vector bornology (category Topological vector spaces)
bounded then f {\displaystyle f} is called a bornological isomorphism. Let X {\displaystyle X} be a vector space over a field K {\displaystyle \mathbb {K}...
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