Theorems · Theorem · functional analysis
LinearMap.withSeminorms_induced
∀ {𝕜 : Type u_2} {𝕜₂ : Type u_3} {E : Type u_6} {F : Type u_7} {ι : Type u_9} [inst : NormedField 𝕜]
[inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E] [inst_3 : NormedField 𝕜₂] [inst_4 : AddCommGroup F]
[inst_5 : Module 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [inst_6 : RingHomIsometric σ₁₂] [inst_7 : TopologicalSpace F]
{q : SeminormFamily 𝕜₂ F ι}, WithSeminorms q → ∀ (f : E →ₛₗ[σ₁₂] F), WithSeminorms (q.comp f)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- Filterproof · cited by 8,121
- nhdsproof · cited by 5,554
- iInfproof · cited by 1,690
- map_zeroproof · cited by 1,614
- IsTopologicalAddGroupproof · cited by 1,394
- NormedFieldstatement and proof · cited by 1,084
Cited by5
Results whose statement or proof uses this declaration.
- Topology.IsInducing.withSeminormsproof · cited by 4
- withSeminorms_piproof · cited by 3
- LinearMap.weakBilin_withSeminormsproof · cited by 2
- ContDiffMapSupportedIn.withSeminormsproof · cited by 1
- PolynormableSpace.inducedproof · cited by 0