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...

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

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...

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

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

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

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...

the definitions of many classes of topological vector spaces, particularly bornological spaces. If X {\displaystyle X} is a TVS then a subset S {\displaystyle...

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

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

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

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

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...

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 Bounded linear operator – Linear transformation between topological vector spacesPages...

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

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...

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

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

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

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

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...

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

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

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

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

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

vector space is a Banach disk. A Hausdorff locally convex space that is sequentially complete and bornological is ultrabornological. Every complete space is...

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