Theorems · Theorem · functional analysis
Bornology.isVonNBounded_singleton
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E] (x : E), Bornology.IsVonNBounded 𝕜 {x}Singletons are bounded.
- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 2 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.
Cites10
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
- nhdsproof · cited by 5,554
- NormedFieldstatement and proof · cited by 1,084
- ContinuousSMulstatement and proof · cited by 1,016
- Bornology.IsVonNBoundedstatement · cited by 136
- absorbent_nhds_zeroproof · cited by 16
- Absorbent.absorbsproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Bornology.sUnion_isVonNBounded_eq_univproof · cited by 3
- Bornology.vonNBornologyproof · cited by 2
- Bornology.IsVonNBounded.vaddproof · cited by 1