Structures · Analysis
BarrelledSpace
A topological vector space E is said to be barrelled if all lower semicontinuous
seminorms on E are actually continuous. This is not the usual definition for TVS over ℝ or ℂ,
but this has the big advantage of working and giving sensible results over any
NontriviallyNormedField. In particular, the Banach-Steinhaus theorem holds for maps between such
a space and any space whose topology is generated by a family of seminorms.
- Defined in
- Mathlib.Analysis.LocallyConvex.Barrelled
- Shape
- 2 explicit arguments · adds continuous_of_lowerSemicontinuous
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