vector space (TVS) is said to be countably barrelled if every weakly bounded countable union of equicontinuous subsets of its continuous dual space is again...

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...

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

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

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

In mathematics, a topological space X {\displaystyle X} is said to be a Baire space if countable unions of closed sets with empty interior also have empty...

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

meagre subsets of a fixed space form a σ-ideal of subsets; that is, any subset of a meagre set is meagre, and the union of countably many meagre sets is meagre...

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...

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...

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

space that is complete (and so sequentially complete) but neither barrelled nor bornological. Bornological spaces need not be barrelled and barrelled...

0\right\}} is necessarily countable (that is, either finite or countably infinite); in other words, all but at most countably many r i {\displaystyle r_{i}}...

locally convex spaces are also paracompact normal reflexive barrelled spaces. The strong dual spaces of both S ( R n ) {\displaystyle {\mathcal {S}}\left(\mathbb...

condition, where the dual space is endowed with the topology of uniform convergence on totally bounded sets. Montel space: a barrelled space where every closed...

X_{b(X^{\prime },X)}^{\prime }} is complete. If X {\displaystyle X} is a barrelled space, then its topology coincides with the strong topology β ( X , X ′ )...

Press. Husain, Taqdir; Khaleelulla, S. M. (1978). Barrelledness in Topological and Ordered Vector Spaces. Lecture Notes in Mathematics. Vol. 692. Berlin...

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...

ISBN 978-0-387-89488-1. Husain, Taqdir (1978). Barrelledness in topological and ordered vector spaces. Berlin New York: Springer-Verlag. ISBN 3-540-09096-7...

in functions More generally, on any compactly generated space; e.g., a first-countable space. Rudin 1991, p. 44 §2.5. Reed & Simon (1980), p. 29; Rudin...

right Haar measure on a locally compact group G {\displaystyle G} is a countably additive measure μ defined on the Borel sets of G {\displaystyle G} which...

residence in Benin City. ——— (1967). "Some remarks on countably barrelled and countably quasibarrelled spaces". Proceedings of the Edinburgh Mathematical Society...

and Y {\displaystyle Y} are barrelled spaces and Z {\displaystyle Z} is locally convex. X {\displaystyle X} is a F-space, Y {\displaystyle Y} is metrizable...

C_{c}^{k}(U),} as well as its strong dual space, is a complete Hausdorff locally convex barrelled bornological Mackey space. The strong dual of C c k ( U ) {\displaystyle...

OCLC 589250. Husain, Taqdir; Khaleelulla, S. M. (1978). Barrelledness in Topological and Ordered Vector Spaces. Lecture Notes in Mathematics. Vol. 692. Berlin...

ISBN 978-0201029857. Husain, Taqdir; Khaleelulla, S. M. (1978). Barrelledness in Topological and Ordered Vector Spaces. Lecture Notes in Mathematics. Vol. 692. Berlin...

OCLC 886098. Husain, Taqdir; Khaleelulla, S. M. (1978). Barrelledness in Topological and Ordered Vector Spaces. Lecture Notes in Mathematics. Vol. 692. Berlin...

everywhere). The space of all Henstock–Kurzweil-integrable functions is often endowed with the Alexiewicz norm, with respect to which it is barrelled but incomplete...

OCLC 589250. Husain, Taqdir; Khaleelulla, S. M. (1978). Barrelledness in Topological and Ordered Vector Spaces. Lecture Notes in Mathematics. Vol. 692. Berlin...