In mathematics, particularly in functional analysis, a bornological space is a type of space which, in some sense, possesses the minimum amount of structure...

normed space). Bornological spaces are exactly those locally convex spaces for which every bounded linear operator into another locally convex space is necessarily...

of the key motivations behind bornologies and bornological analysis is the fact that bornological spaces provide a convenient setting for homological algebra...

bounded. Bornological space – Space where bounded operators are continuous Bounded operator – Linear transformation between topological vector spaces Bounded...

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...

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...

Barrelled space Bornological space Bourbaki–Alaoglu theorem Dual pair F-space Fréchet space Krein–Milman theorem Locally convex topological vector space Mackey...

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...

convex space is continuous. The space ( X , τ lc ) {\displaystyle \left(X,\tau _{\operatorname {lc} }\right)} is a bornological space. Every normed space is...

0<p<1.} Barrelled spaces: locally convex spaces where the Banach–Steinhaus theorem holds. Bornological space: a locally convex space where the continuous...

reflexive nuclear Montel bornological barrelled Mackey space; the same is true of its strong dual space (that is, the space of all distributions with...

quasi-ultrabarrelled space, and a bornological space but there exist bornological spaces that are not ultrabornological. Every ultrabornological space X {\displaystyle...

Bornological space – Space where bounded operators are continuous Bounded linear operator – Linear transformation between topological vector spacesPages...

Montel spaces having closed vector subspaces that are not Montel spaces. Barrelled space – Type of topological vector space Bornological space – Space where...

each of these three spaces, are complete nuclear Montel bornological spaces, which implies that all six of these locally convex spaces are also paracompact...

variable Publisher: R. E. Krieger Pub. Co (1977) ISBN 0-88275-531-5 Bornological space "George Mackey - The Mathematics Genealogy Project". www.mathgenealogy...

quasibarrelled DF-space that is not bornological. There exists a quasibarrelled space that is not a σ-barrelled space. Barrelled space – Type of topological...

{\displaystyle 0_{R}} such that w A ⊆ B . {\displaystyle wA\subseteq B.} Bornological space – Space where bounded operators are continuous Bornivorous set – A set...

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...

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...

families are independence systems, greedoids, antimatroids, and bornological spaces. Algebra of sets – Identities and relationships involving sets Class...

spaces that are Mackey spaces include: All barrelled spaces and more generally all infrabarreled spaces Hence in particular all bornological spaces and...

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...

Bornological space – Space where bounded operators are continuous Injective tensor product Locally convex topological vector space – A vector space with...

bornological space. All normed spaces and semi-reflexive spaces are distinguished spaces. LF spaces are distinguished spaces. The strong dual space X...

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)}}...

linear operator between Banach spaces for which the image of the unit ball is bounded. bornological A bornological space. Birkhoff orthogonality Two vectors...

examples are the following. The category of (possibly non-Hausdorff) bornological spaces is semiabelian. Let Q {\displaystyle Q} be the quiver 1 → 2 ← 3 ↓...

convex spaces (such as Fréchet spaces) is necessarily complete. In particular, every LF-space is complete. Every LF-space is barrelled and bornological, which...

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}...