Theorems · Theorem · functional analysis
WithSeminorms.isVonNBounded_iff_seminorm_bounded
∀ {𝕜 : Type u_2} {E : Type u_6} {ι : Type u_9} [inst : NontriviallyNormedField 𝕜] [inst_1 : AddCommGroup E]
[inst_2 : Module 𝕜 E] {p : SeminormFamily 𝕜 E ι} [inst_3 : TopologicalSpace E] {s : Set E},
WithSeminorms p → (Bornology.IsVonNBounded 𝕜 s ↔ ∀ (i : ι), ∃ r > 0, ∀ x ∈ s, (p i) x < r)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Finsetproof · cited by 13,712
- AddCommGroupstatement and proof · cited by 12,871
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Finset.Nonemptyproof · cited by 1,001
- Eq.leproof · cited by 605
- zero_lt_oneproof · cited by 598
- DFunLikeproof · cited by 576
Cited by4
Results whose statement or proof uses this declaration.
- withSeminorms_iff_mem_nhds_isVonNBoundedproof · cited by 1
- WithSeminorms.isVonNBounded_iff_seminorm_bddAboveproof · cited by 1
- WithSeminorms.image_isVonNBounded_iff_seminorm_boundedproof · cited by 0
- WeakDual.isBounded_iff_isVonNBoundedproof · cited by 0