Ultra-barrelled space

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2020 Mathematics Subject Classification: Primary: 46A [MSN][ZBL]

A topological vector space $E$ with a topology $\mathfrak{T}$ for which any topology $\mathfrak{T}'$ having a neighbourhood base of zero consisting of $\mathfrak{T}$-closed sets is weaker than $\mathfrak{T}$. Every topological vector space which is not a set of the first category is ultra-barrelled. If a locally convex space is ultra-barrelled, it is also barrelled, but a barrelled space need not be ultra-barrelled.


[1] R.E. Edwards, "Functional analysis: theory and applications" , Holt, Rinehart & Winston (1965)
[2] W.S. Robertson, "Completions of topological vector spaces" Proc. London Math. Soc. , 8 : 30 (1958) pp. 242–257
How to Cite This Entry:
Ultra-barrelled space. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.I. Lomonosov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article