Theorems · Theorem · functional analysis
NormedSpace.isVonNBounded_iff
∀ (𝕜 : Type u_1) {E : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : SeminormedAddCommGroup E]
[inst_2 : NormedSpace 𝕜 E] {s : Set E}, Bornology.IsVonNBounded 𝕜 s ↔ Bornology.IsBounded s- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 9 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.
Cites21
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
- Realproof · 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.ballproof · cited by 735
- zero_lt_oneproof · cited by 598
- LT.lt.transproof · cited by 370
- Bornology.IsBoundedstatement · cited by 293
- norm_pos_iffproof · cited by 168
Cited by9
Results whose statement or proof uses this declaration.
- ZLattice.covolume.tendsto_card_div_pow''proof · cited by 2
- ZLattice.covolume.tendsto_card_le_div''proof · cited by 2
- NormedSpace.isVonNBounded_iff'proof · cited by 1
- NormedSpace.isBounded_iff_subset_smul_ballproof · cited by 1
- NormedSpace.isBounded_iff_subset_smul_closedBallproof · cited by 1
- IsCompactOperator.image_subset_compact_of_boundedproof · cited by 0
- IsCompactOperator.isCompact_closure_image_of_boundedproof · cited by 0
- WeakDual.isBounded_iff_isVonNBoundedproof · cited by 0
- NormedSpace.vonNBornology_eqproof · cited by 0