countably quasi-barrelled space is a σ-quasi-barrelled space. Every barrelled space, every countably barrelled space, and every quasi-barrelled space...

Every countably barrelled space is a countably quasibarrelled space, a σ-barrelled space, a σ-quasi-barrelled space, and a sequentially barrelled space. An...

vector. A barrelled set or a barrel in a topological vector space is a set that is convex, balanced, absorbing, and closed. Barrelled spaces are studied...

descriptions of redirect targets Countably quasi-barrelled space Complete metric space – Metric geometry Complete topological vector space – A TVS where points that...

X} is a DF-space, also written (DF)-space, if X {\displaystyle X} is a countably quasi-barrelled space (i.e. every strongly bounded countable union of equicontinuous...

barrelled. Barrelled space – Type of topological vector space Countably barrelled space Countably quasi-barrelled space Infrabarreled space Uniform boundedness...

quasi-ultrabarrelled. Barrelled space Countably barrelled space Countably quasi-barrelled space Infrabarreled space Ultrabarrelled space Uniform boundedness...

space that is sequentially complete is barrelled. A locally convex Hausdorff quasibarrelled space is a Mackey space, quasi-M-barrelled, and countably...

(X^{\prime },X)} is quasi-barrelled. β ( X ′ , X ) {\displaystyle \beta (X^{\prime },X)} is barrelled. X {\displaystyle X} is a distinguished space. If L : X →...

Banach space cannot be the union of countably many closed subspaces, unless it is already equal to one of them; a Banach space with a countable Hamel basis...

semi-reflexive countably barrelled space that is not barrelled. Grothendieck space - A generalization which has some of the properties of reflexive spaces and includes...

TVSs of a family of bornological (resp. barrelled, quasi-barrelled) spaces has this same property. Every LF-space is a meager subset of itself. The strict...

property. A nuclear quasi-complete barrelled space is a Montel space. Every closed equicontinuous subset of the dual of a nuclear space is a compact metrizable...

spaces that are not Schwartz spaces and there exist Schwartz spaces that are not Montel spaces. Auxiliary normed space Montel space – Barrelled space...

complete. If X {\displaystyle X} is barrelled then L G ( X ; Y ) {\displaystyle L_{\mathcal {G}}(X;Y)} is Hausdorff and quasi-complete. Let X {\displaystyle...

result can be extended to the class of all quasi-complete barreled spaces (in particular, to all Fréchet spaces). In the 1990s Sergei Akbarov gave a description...

not quasi-complete. If a TVS has a complete neighborhood of the origin then it is complete. Every complete pseudometrizable TVS is a barrelled space and...

an LB-space, also written (LB)-space, is a topological vector space X {\displaystyle X} that is a locally convex inductive limit of a countable inductive...