Theorems · Theorem · functional analysis
NormedSpace.isVonNBounded_of_isBounded
∀ (𝕜 : Type u_1) {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E]
{s : Set E}, Bornology.IsBounded s → Bornology.IsVonNBounded 𝕜 s- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- NormedFieldstatement and proof · cited by 1,084
- Metric.ballproof · cited by 735
- Bornology.IsBoundedstatement and proof · cited by 293
- Bornology.IsVonNBoundedstatement · cited by 136
- Absorbsproof · cited by 59
- Metric.nhds_basis_ballproof · cited by 41
- normSeminormproof · cited by 32
- ball_normSeminormproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- NormedSpace.isVonNBounded_iffproof · cited by 9
- NormedSpace.isVonNBounded_closedBallproof · cited by 5
- NormedSpace.isVonNBounded_ballproof · cited by 4
- exists_homeomorph_image_interior_closure_frontier_eq_unitBallproof · cited by 0