Theorems · Theorem · functional analysis
Set.Finite.isVonNBounded
∀ {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] {s : Set E}, s.Finite → Bornology.IsVonNBounded 𝕜 sFinite sets are bounded.
- Defined in
- Mathlib.Analysis.LocallyConvex.Bounded
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
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
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- nhdsproof · cited by 5,554
- Set.Finitestatement and proof · cited by 1,814
- NormedFieldstatement and proof · cited by 1,084
- ContinuousSMulstatement and proof · cited by 1,016
- Bornology.IsVonNBoundedstatement · cited by 136
- absorbent_nhds_zeroproof · cited by 16
- Absorbent.absorbs_finiteproof · cited by 1
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