Theorems · Theorem · functional analysis
nhds_basis_balanced
∀ (𝕜 : Type u_1) (E : Type u_2) [inst : NormedDivisionRing 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E] [(nhdsWithin 0 {0}ᶜ).NeBot],
(nhds 0).HasBasis (fun s => s ∈ nhds 0 ∧ Balanced 𝕜 s) id- Cited by
- 10 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Filterstatement · cited by 8,121
- nhdsstatement and proof · cited by 5,554
- Compl.complstatement and proof · cited by 2,925
- nhdsWithinstatement and proof · cited by 1,912
- ContinuousSMulstatement and proof · cited by 1,016
- Filter.NeBotstatement and proof · cited by 853
- Filter.HasBasisstatement · cited by 604
- NormedDivisionRingstatement and proof · cited by 360
Cited by10
Results whose statement or proof uses this declaration.
- Asymptotics.isLittleOTVS_oneproof · cited by 4
- TotallyBounded.isVonNBoundedproof · cited by 4
- Asymptotics.IsLittleOTVS.prodMkproof · cited by 2
- Asymptotics.IsBigOTVS.prodMkproof · cited by 2
- Bornology.isVonNBounded_of_smul_tendsto_zeroproof · cited by 2
- ContinuousSMul.topology_eq_of_nhds_inf_principal_eqproof · cited by 1
- LinearMap.continuousAt_zero_of_locally_boundedproof · cited by 1
- Asymptotics.IsLittleOTVS.piproof · cited by 1
- Asymptotics.IsBigOTVS.piproof · cited by 1
- Asymptotics.Filter.Tendsto.isBigOTVS_oneproof · cited by 1