Theorems · Theorem · functional analysis
nhds_basis_closed_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] [RegularSpace E],
(nhds 0).HasBasis (fun s => s ∈ nhds 0 ∧ IsClosed s ∧ Balanced 𝕜 s) id- Cited by
- 0 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
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
- IsClosedstatement and proof · cited by 1,639
- ContinuousSMulstatement and proof · cited by 1,016
- Filter.NeBotstatement and proof · cited by 853
- Filter.HasBasisstatement · cited by 604
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