Theorems · Theorem · functional analysis
Bornology.IsVonNBounded.subset
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : SeminormedRing 𝕜] [inst_1 : SMul 𝕜 E] [inst_2 : Zero E]
[inst_3 : TopologicalSpace E] {s₁ s₂ : Set E}, s₁ ⊆ s₂ → Bornology.IsVonNBounded 𝕜 s₂ → Bornology.IsVonNBounded 𝕜 s₁Subsets of bounded sets are bounded.
- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- nhdsproof · cited by 5,554
- SeminormedRingstatement and proof · cited by 446
- Bornology.IsVonNBoundedstatement and proof · cited by 136
- Absorbs.mono_rightproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Bornology.IsVonNBounded.of_add_rightproof · cited by 3
- NormedSpace.isBounded_iff_subset_smul_ballproof · cited by 1
- NormedSpace.isBounded_iff_subset_smul_closedBallproof · cited by 1