Theorems · Theorem · functional analysis
NormedSpace.isBounded_iff_subset_smul_ball
∀ (𝕜 : Type u_1) {E : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : SeminormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {s : Set E}, Bornology.IsBounded s ↔ ∃ a, s ⊆ a • Metric.ball 0 1- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Realstatement and proof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Norm.normproof · cited by 5,413
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- LT.lt.leproof · cited by 2,189
- Metric.ballstatement and proof · cited by 735
- Set.smulSetstatement · cited by 608
- zero_lt_oneproof · cited by 598
- Bornology.IsBoundedstatement · cited by 293
- Bornology.IsVonNBoundedproof · cited by 136
Cited by1
Results whose statement or proof uses this declaration.
- NormedSpace.isBounded_iff_subset_smul_closedBallproof · cited by 1