Theorems · Theorem · functional analysis
exists_nhds_hasAntitoneBasis_absConvex_open_add_closure_subset
∀ (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] [FirstCountableTopology E],
∃ x,
(nhds 0).HasAntitoneBasis x ∧
∀ (n : ℕ), IsOpen (x n) ∧ AbsConvex 𝕜 (x n) ∧ x (n + 1) + x (n + 1) ⊆ x n ∧ closure (x (n + 1)) ⊆ x n- Defined in
- Mathlib.Analysis.LocallyConvex.AbsConvex
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites47
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- PartialOrderstatement and proof · cited by 6,410
- nhdsstatement and proof · cited by 5,554
- LE.le.transproof · cited by 3,151
- IsOpenstatement and proof · cited by 2,400
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.