Theorems · Theorem · functional analysis
Bornology.sUnion_isVonNBounded_eq_univ
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : TopologicalSpace E] [ContinuousSMul 𝕜 E], ⋃₀ Set.ofPred (Bornology.IsVonNBounded 𝕜) = Set.univThe union of all bounded set is the whole space.
- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Set.ofPredstatement · cited by 6,101
- Set.univstatement · cited by 3,945
- NormedFieldstatement and proof · cited by 1,084
- ContinuousSMulstatement and proof · cited by 1,016
- Set.sUnionstatement · cited by 392
- Set.mem_singletonproof · cited by 183
- Bornology.IsVonNBoundedstatement · cited by 136
- Set.eq_univ_iff_forallproof · cited by 93
Cited by3
Results whose statement or proof uses this declaration.
- ContinuousMultilinearMap.uniformContinuous_coe_funproof · cited by 2
- ContinuousMultilinearMap.completeSpaceproof · cited by 1
- ContinuousLinearMap.completeSpaceproof · cited by 0