Theorems · Theorem · functional analysis
Absorbent.subset_range_iff_surjective
∀ {𝕜 : Type u_1} {E : Type u_3} [inst : NontriviallyNormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
{F : Type u_8} {𝕜₂ : Type u_9} [inst_3 : Semiring 𝕜₂] {σ : 𝕜₂ →+* 𝕜} [inst_4 : AddCommGroup F] [inst_5 : Module 𝕜₂ F]
[inst_6 : RingHomSurjective σ] {f : F →ₛₗ[σ] E} {s : Set E}, Absorbent 𝕜 s → (s ⊆ ↑f.range ↔ Function.Surjective ⇑f)- Defined in
- Mathlib.Analysis.LocallyConvex.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 126 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.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- SetLike.coestatement and proof · cited by 8,199
- Submodulestatement · cited by 7,192
- LinearMap.rangestatement and proof · cited by 893
- RingHomSurjectivestatement and proof · cited by 220
Cited by1
Results whose statement or proof uses this declaration.
- ball_zero_subset_range_iff_surjectiveproof · cited by 1