Theorems · Theorem · functional analysis

nhds_hasBasis_absConvex_closed

∀ (𝕜 : Type u_1) (E : Type u_2) [inst : NontriviallyNormedField 𝕜] [inst_1 : PartialOrder 𝕜] [inst_2 : AddCommGroup E]
  [inst_3 : Module 𝕜 E] [inst_4 : TopologicalSpace E] [LocallyConvexSpace 𝕜 E] [ContinuousSMul 𝕜 E]
  [IsTopologicalAddGroup E] [ZeroLEOneClass 𝕜], (nhds 0).HasBasis (fun s => s ∈ nhds 0 ∧ IsClosed s ∧ AbsConvex 𝕜 s) id

Defined in: Mathlib.Analysis.LocallyConvex.AbsConvex
Cited by: 0 results in Mathlib
Foundations: Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NontriviallyNormedField PartialOrder AddCommGroup Module TopologicalSpace LocallyConvexSpace ContinuousSMul IsTopologicalAddGroup ZeroLEOneClass

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Setstatement and proof · cited by 53,352
TopologicalSpacestatement and proof · cited by 24,529
Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
NontriviallyNormedFieldstatement and proof · cited by 8,742
Filterstatement · cited by 8,121
PartialOrderstatement and proof · cited by 6,410
nhdsstatement and proof · cited by 5,554
LE.le.transproof · cited by 3,151
IsOpenproof · cited by 2,400
IsClosedstatement and proof · cited by 1,639
IsTopologicalAddGroupstatement and proof · cited by 1,394

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