Theorems · Theorem · functional analysis
Bornology.isVonNBounded_add_self
∀ {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] [ContinuousAdd E] {s : Set E},
Bornology.IsVonNBounded 𝕜 (s + s) ↔ Bornology.IsVonNBounded 𝕜 s- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- Set.Nonemptyproof · cited by 2,627
- NormedFieldstatement and proof · cited by 1,084
- ContinuousSMulstatement and proof · cited by 1,016
- ContinuousAddstatement and proof · cited by 777
- Set.addstatement · cited by 338
- Set.eq_empty_or_nonemptyproof · cited by 248
- Bornology.IsVonNBoundedstatement and proof · cited by 136
- Set.add_emptyproof · cited by 4
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